Number Theory

Problem 401

Complete the prime factor tree for 21 and find its prime factors. Also, determine the LCM of 14 and 21.

See Solution

Problem 402

Find the prime factorization of 72. $72 = 2^{3} \cdot 3^{2}$

See Solution

Problem 403

Find the prime factorization of 150. $150=$ $2 \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 25$ $2^{3} \cdot 3 \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5^{2}$

See Solution

Problem 404

Find the prime factorization of 136.

See Solution

Problem 405

A teacher has 36 students. What is the maximum number of equal groups possible? Also, state the rule for divisibility by 2.

See Solution

Problem 406

Identify the composite numbers from the list: 2, 15, 4, 3, 5, 9. Select all that apply.

See Solution

Problem 407

Identify the prime numbers from this list: 11, 6, 1, 9, 2, 21. Select ALL that apply.

See Solution

Problem 408

Identify the prime numbers from this list: 53, 29, 51, 49, 57, 39.

See Solution

Problem 409

Identify the prime numbers from this list: 2, 21, 1, 11, 9, 64. Select ALL that apply.

See Solution

Problem 410

Identify the prime numbers from this list: 2, 3, 4, 7, 13, 15, 22, 23, 24, 28.

See Solution

Problem 411

Identify the prime numbers from this list: 31, 29, 40. Select ALL that are prime.

See Solution

Problem 412

Find the prime factorization of 120 using exponents for repeats, e.g., $2^{\wedge} 3^{\star} 5$ .

See Solution

Problem 413

Find the prime factorization of 55 using exponents and * for repeated factors, e.g., $5 * 11$ .

See Solution

Problem 414

Determine which numbers are factors of 96 using divisibility rules: 9, 8, 2, 7, 3. Select all that apply.

See Solution

Problem 415

Find the prime factorization of 84 using exponents for repeated factors, like $2^{\wedge} 2^{*} 3$ .

See Solution

Problem 416

Find the prime factorization of 231 using exponents for repeats and * between factors. Example: $2^{\wedge} 2^{*} 3$ .

See Solution

Problem 417

Find the prime factorization for 33, 32, and determine if 19 is prime.

See Solution

Problem 418

Find the prime factorization, GCF, and LCM of two numbers.

See Solution

Problem 419

Berechne die Wahrscheinlichkeit, dass eine Zahl aus den ersten 200 natürlichen Zahlen durch 7 oder 9 teilbar ist.

See Solution

Problem 420

Conjecture the sum of primes based on this pattern: 4=2+2, 6=3+3, 8=3+5, 10=3+7, 12=5+7. What do you observe?

See Solution

Problem 421

Find two different prime numbers that add up to 38. Write the numbers in the boxes above.

See Solution

Problem 422

Determine the prime factorization of 53. Is it $3^{2} \cdot 5$ , $3^{2} \cdot 17$ , $3^{2} \cdot 7$ , or prime?

See Solution

Problem 423

Find the prime factorization of 60. Options: $3 \cdot 4 \cdot 5$ , $3^{2} \cdot 7$ , $2^{2} \cdot 3 \cdot 5$ , or 60 is prime.

See Solution

Problem 424

Write $N=9^{5} \times 15^{5}$ as a product of prime factors in index form.

See Solution

Problem 425

Count the prime numbers in the diagonal squares with 7 in a spiral grid from 1 to 49. Options: (A) 0 (B) 1 (C) 2 (D) 3 (E) 4.

See Solution

Problem 426

In a spiral grid from 1 to 49, how many of the four numbers on the diagonal with 7 are prime? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

See Solution

Problem 427

Find the prime factorization of 93. Format as $a^{b} * c^{d}$ or $a * b * c$ .

See Solution

Problem 428

Find the prime factorization of 48 in the format $a^{b} * c^{d}$ or $a * b * c$ .

See Solution

Problem 429

Identify the factors of 235 from the numbers 2, 3, 5, and 10. Choose all that apply.

See Solution

Problem 430

Find a prime number from this list: 57, 58, 59, 60, 61, 62, 63, 64, 65.

See Solution

Problem 431

Find the GCF of the numbers $150$ , $275$ , and $420$ .

See Solution

Problem 432

List all factors of 12.

See Solution

Problem 433

Create a prime factor tree for 90, then find the HCF of 90 and 252 using it.

See Solution

Problem 434

If 22 divides $n$ , what other natural numbers also divide $n$ ? List them.

See Solution

Problem 435

Find the prime factorization of these: a. $1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8$ , b. $35^{5} \cdot 65 \cdot 9^{15}$ , c. 181, d. $5000^{9}$ .

See Solution

Problem 436

Find the prime factorization of these: a. $1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8$ b. $35^{5} \cdot 65 \cdot 9^{15}$ c. 181 d. $5000^{9}$

See Solution

Problem 437

Find the GCD and LCM using prime factorization for these pairs: a. 140 & 2200, b. 26 & 1690, c. 96, 1764 & 630, d. 200 & 1500.

See Solution

Problem 438

Find the prime factorization of 77.

See Solution

Problem 439

Identify the group that contains only prime numbers: A. $45,55,65,76$ B. $31,37,61,57$ C. $29,33,73,89$ D. $23,41,53,59$

See Solution

Problem 440

Find the factors of 21 and 27, then calculate the GCF(21, 27).

See Solution

Problem 441

Find the prime factorization of 55 using the tree method. Use exponents for repeated factors and * between factors.

See Solution

Problem 442

Find all divisors of 84.

See Solution

Problem 443

Find the prime factorization of 210. Options: $6 \cdot 5 - 7$ , $2 \cdot 3 \cdot 35$ , $3 \cdot 7 \cdot 10$ , $2 \cdot 3 \cdot 5 \cdot 7$ .

See Solution

Problem 444

Find the prime factorization of 144. Options: $2^{3}+3^{4}$ , $2^{2}+3^{5}$ , $2^{4} \cdot 3^{2}$ , $2^{4}+3^{4}$ .

See Solution

Problem 445

Find the prime factors, LCM, and GCF for 44 and 66. Prime factors: $44=$ , $66=$ , $\mathrm{LCM}=$ .

See Solution

Problem 446

Find the prime factors of 44 and 66, then determine their GCF and list all factors in order.

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Problem 447

Selecciona verdadero o falso:
1. La negación de "si los cerdos vuelan, lo creeré" es "si los cerdos no vuelan, no lo creeré".
2. Todos los números enteros son racionales.
3. $3/5$ es irracional.
4. Existe un número que es racional e irracional.

See Solution

Problem 448

Complete the prime factorization of 180 and express your answer in index form: $180 = 2^a \times 3^b \times 5^c$ .

See Solution

Problem 449

Find the prime decomposition of 1197 in index form using the prime factor tree provided.

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Problem 450

Write 200 as a product of its prime factors using index notation.

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Problem 451

Factor 132 into its prime components.

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Problem 452

Find the HCF of 90 and 396. Create a prime factor tree for 90. Use the given tree for 396: 2, 198, 2, 99, 3, 33, 3, 11.

See Solution

Problem 453

Find the HCF of 42 and 231 using prime factor trees. Factors: 42 is $2 \times 3 \times 7$ , 231 is $3 \times 7 \times 11$ .

See Solution

Problem 454

Draw prime factor trees for 40 and 220, then find their lowest common multiple (LCM).

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Problem 455

Mrs. Robbins has 54 students. Which arrangement is NOT possible? A. 2 rows of 27, B. 3 rows of 18, C. 4 rows of 13?

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Problem 456

Find the HCF and LCM of $A=2^{6} \times 3^{5} \times 7$ and $B=2^{7} \times 3^{8} \times 5$ in prime factor form.

See Solution

Problem 457

Factor the following numbers into primes or state they are prime: 20. 154, 21. 95, 22. 178.

See Solution

Problem 458

Find the greatest common factor of 15 and 60. Use a factor tree for each number and organize primes in a Venn diagram.

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Problem 459

Find the prime factorization of 612. Use exponents for repeated factors.

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Problem 460

1. Find the volume of a cube.
2. a. Identify perfect squares from: 16, 125, 20, 144, 25, 225, 100, 10,000. b. Explain your reasoning.
3. a. Identify perfect cubes from: 1, 3, 8, 9, 27, 64, 100, 125.

See Solution

Problem 461

Find the prime factorization of 684, using exponents for repeated factors.

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Problem 462

List all factors of 10.

See Solution

Problem 463

Find the greatest common factor (GCF) for: 1. 7 and 3 2. 14 and 42.

See Solution

Problem 464

Find the LCM of 35, 105, and an unknown number.

See Solution

Problem 465

Find the prime factors of 828.

See Solution

Problem 466

¿Cuál número tiene como factores primos a $3^{2} \cdot 5$ ? a. 11 b. 30 c. 45 d. 42

See Solution

Problem 467

¿Cuál es la factorización prima de 24? a. $2 \bullet 3 \bullet 4$ b. $6 \bullet 4$ c. $2^{3} \bullet 3$ d. $2^{2} \cdot 3^{2}$

See Solution

Problem 468

Encuentra la factorización prima de $120$ . a. $2^{2} \cdot 25 \bullet 4^{2}$ b. $6 \bullet 4 \bullet 5$ c. $2 \cdot 5 \bullet 12$ d. $2^{3} \cdot 3 \cdot 5$

See Solution

Problem 469

List all factors of 99. Options: $1, 3, 9, 11, 33, 99$ .

See Solution

Problem 470

Identify the correct prime factorization of 360 in exponential form:
1) $2 \cdot 3^{2} \cdot 5$ 2) $2 \cdot 3 \cdot 5$ 3) $2^{3} \cdot 3^{2} \cdot 5^{2}$ 4) $2^{3} \cdot 3^{2} \cdot 5$

See Solution

Problem 471

After how many seconds will a yellow light (8s), blue light (9s), and red light (12s) flash together again?

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Problem 472

Calculate the LCM of 18 and 315 using their prime factors.

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Problem 473

Find the highest common factor (HCF) of 825 and 950 using their prime factor trees: $825 = 3 \times 5^2 \times 11$ , $950 = 2 \times 5^2 \times 19$ .

See Solution

Problem 474

Check all the prime numbers: 8, 9, 13, 17, 22, 23, or None of the above.

See Solution

Problem 475

Find the LCM and HCF of $C = 2^{8} \times 3^{4} \times 5$ and $D = 2^{4} \times 3^{3} \times 5 \times 7$ .

See Solution

Problem 476

What is the longest length in metres ( $\mathrm{m}$ ) for equal pieces cut from 27 m of red wire and 12 m of black wire?

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Problem 477

Find the prime factorization of 396 in index form and identify which two of these are factors: 88, 14, 121, 9, 22.

See Solution

Problem 478

Find the prime factorization of 252 in index form and identify which of these are factors: 22, 24, 9, 14, 49.

See Solution

Problem 479

Identify the non-factor in each set: a) 14 $\{1,2,4,7,14\}$ b) 15 $\{1,3,5,15,45\}$ c) 21 $\{1,3,7,14,21\}$ d) 33 $\{1,3,11,22,33\}$ e) 42 $\{3,6,7,8,14\}$

See Solution

Problem 480

Find the prime factorization of 84.

See Solution

Problem 481

Find the greatest number of identical platters Mitchell can prepare using 18 pieces of chocolate cake and 8 pieces of cheesecake.

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Problem 482

Write each composite number as the sum of two prime numbers, e.g., $6=3+3$ and $8=3+5$ .

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Problem 483

Find the GCF of the numbers 15, 45, and 100. The GCF is $$.

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Problem 484

i) Identify the imaginary numbers: $\sqrt{-2}, \sqrt{-\frac{1}{\sqrt{2}}}, -\sqrt{7}$ . ii) Show that $0.\overline{21}$ and $21\%$ are the same as a fraction. iii) Determine if $\sqrt{2} \cdot \sqrt{8}, \sqrt{\frac{8}{2}}, \sqrt{2}+\sqrt{8}$ are irrational. iv) Verify if $\sqrt{9}+\sqrt{16}+\sqrt{9+16}=\sqrt{9 \cdot 16}$ . v) Prove that $|-3-|-7||>||-3|-7|$ .

See Solution

Problem 485

Find the smallest prime $p$ such that $p^{2}+p+1$ is not prime.

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Problem 486

Draw the prime factor tree for 42 and find the HCF of 42 and 390 using it.

See Solution

Problem 487

Draw the prime factor tree for 70 and find the highest common factor (HCF) of 70 and 546.

See Solution

Problem 488

Find the prime factorization of these numbers: a. $1 \cdot 2 \cdots 12$ b. $33^{3} \cdot 39 \cdot 25^{11}$ c. 199 d. $10000^{8}$

See Solution

Problem 489

Find the GCD and LCM using prime factorization for: a. 60, 792; b. 39, 1014; c. 160, 4900, 1050; d. 200, 1500.

See Solution

Problem 490

If 22 divides $n$ , what other natural numbers divide $n$ ? List them and explain why.

See Solution

Problem 491

Find the GCF for these pairs: 18 & 27, 35 & 49, 30 & 21, 24 & 36.

See Solution

Problem 492

Complete the prime factor tree for 1078 and express it as a product of primes in index form.

See Solution

Problem 493

Find the prime factorization of 396 in index form.

See Solution

Problem 494

Find the greatest common divisor (GCD) of 6 and 10.

See Solution

Problem 495

Find the highest common factor (HCF) of 9 and 15: calculate $HCF(9, 15)$ .

See Solution

Problem 496

Create a prime factor tree for 60, then find the highest common factor (HCF) of 60 and 468.

See Solution

Problem 497

Draw a prime factor tree for 66 and express it as a product of its prime factors.

See Solution

Problem 498

Find the prime decomposition of 1683 in index form using the prime factor tree provided.

See Solution

Problem 499

Find the prime factorization of 60 and express it in index form.

See Solution

Problem 500

Find the prime factors of 136 in the form $2^{a} \times b$ and determine the values of $a$ and $b$ .

See Solution

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Number Theory

Problem 401

Complete the prime factor tree for 21 and find its prime factors. Also, determine the LCM of 14 and 21.

Problem 402

Find the prime factorization of 72. 72=23⋅32 72 = 2^{3} \cdot 3^{2} 72=23⋅32

Problem 403

Find the prime factorization of 150. 150= 150= 150= 2⋅3⋅522 \cdot 3 \cdot 5^{2}2⋅3⋅52 2⋅3⋅252 \cdot 3 \cdot 252⋅3⋅25 23⋅3⋅52^{3} \cdot 3 \cdot 523⋅3⋅5 23⋅32⋅522^{3} \cdot 3^{2} \cdot 5^{2}23⋅32⋅52

Problem 404

Find the prime factorization of 136.

Problem 405

A teacher has 36 students. What is the maximum number of equal groups possible? Also, state the rule for divisibility by 2.

Problem 406

Identify the composite numbers from the list: 2, 15, 4, 3, 5, 9. Select all that apply.

Problem 407

Identify the prime numbers from this list: 11, 6, 1, 9, 2, 21. Select ALL that apply.

Problem 408

Identify the prime numbers from this list: 53, 29, 51, 49, 57, 39.

Problem 409

Identify the prime numbers from this list: 2, 21, 1, 11, 9, 64. Select ALL that apply.

Problem 410

Identify the prime numbers from this list: 2, 3, 4, 7, 13, 15, 22, 23, 24, 28.

Problem 411

Identify the prime numbers from this list: 31, 29, 40. Select ALL that are prime.

Problem 412

Find the prime factorization of 120 using exponents for repeats, e.g., 2∧3⋆52^{\wedge} 3^{\star} 52∧3⋆5.

Problem 413

Find the prime factorization of 55 using exponents and * for repeated factors, e.g., 5∗115 * 115∗11.

Problem 414

Determine which numbers are factors of 96 using divisibility rules: 9, 8, 2, 7, 3. Select all that apply.

Problem 415

Find the prime factorization of 84 using exponents for repeated factors, like 2∧2∗32^{\wedge} 2^{*} 32∧2∗3.

Problem 416

Find the prime factorization of 231 using exponents for repeats and * between factors. Example: 2∧2∗32^{\wedge} 2^{*} 32∧2∗3.

Problem 417

Find the prime factorization for 33, 32, and determine if 19 is prime.

Problem 418

Find the prime factorization, GCF, and LCM of two numbers.

Problem 419

Berechne die Wahrscheinlichkeit, dass eine Zahl aus den ersten 200 natürlichen Zahlen durch 7 oder 9 teilbar ist.

Problem 420

Conjecture the sum of primes based on this pattern: 4=2+2, 6=3+3, 8=3+5, 10=3+7, 12=5+7. What do you observe?

Problem 421

Find two different prime numbers that add up to 38. Write the numbers in the boxes above.

Problem 422

Determine the prime factorization of 53. Is it 32⋅53^{2} \cdot 532⋅5, 32⋅173^{2} \cdot 1732⋅17, 32⋅73^{2} \cdot 732⋅7, or prime?

Problem 423

Find the prime factorization of 60. Options: 3⋅4⋅53 \cdot 4 \cdot 53⋅4⋅5, 32⋅73^{2} \cdot 732⋅7, 22⋅3⋅52^{2} \cdot 3 \cdot 522⋅3⋅5, or 60 is prime.

Problem 424

Write N=95×155N=9^{5} \times 15^{5}N=95×155 as a product of prime factors in index form.

Problem 425

Count the prime numbers in the diagonal squares with 7 in a spiral grid from 1 to 49. Options: (A) 0 (B) 1 (C) 2 (D) 3 (E) 4.

Problem 426

In a spiral grid from 1 to 49, how many of the four numbers on the diagonal with 7 are prime? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Problem 427

Find the prime factorization of 93. Format as ab∗cda^{b} * c^{d}ab∗cd or a∗b∗ca * b * ca∗b∗c.

Problem 428

Find the prime factorization of 48 in the format ab∗cda^{b} * c^{d}ab∗cd or a∗b∗ca * b * ca∗b∗c.

Problem 429

Identify the factors of 235 from the numbers 2, 3, 5, and 10. Choose all that apply.

Problem 430

Find a prime number from this list: 57, 58, 59, 60, 61, 62, 63, 64, 65.

Problem 431

Find the GCF of the numbers 150150150, 275275275, and 420420420.

Problem 432

List all factors of 12.

Problem 433

Create a prime factor tree for 90, then find the HCF of 90 and 252 using it.

Problem 434

If 22 divides nnn, what other natural numbers also divide nnn? List them.

Problem 435

Find the prime factorization of these: a. 1⋅2⋅3⋅4⋅5⋅6⋅7⋅81 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 81⋅2⋅3⋅4⋅5⋅6⋅7⋅8, b. 355⋅65⋅91535^{5} \cdot 65 \cdot 9^{15}355⋅65⋅915, c. 181, d. 500095000^{9}50009.

Problem 436

Find the prime factorization of these: a. 1⋅2⋅3⋅4⋅5⋅6⋅7⋅81 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 81⋅2⋅3⋅4⋅5⋅6⋅7⋅8 b. 355⋅65⋅91535^{5} \cdot 65 \cdot 9^{15}355⋅65⋅915 c. 181 d. 500095000^{9}50009

Problem 437

Find the GCD and LCM using prime factorization for these pairs: a. 140 & 2200, b. 26 & 1690, c. 96, 1764 & 630, d. 200 & 1500.

Problem 438

Find the prime factorization of 77.

Problem 439

Identify the group that contains only prime numbers: A. 45,55,65,7645,55,65,7645,55,65,76 B. 31,37,61,5731,37,61,5731,37,61,57 C. 29,33,73,8929,33,73,8929,33,73,89 D. 23,41,53,5923,41,53,5923,41,53,59

Problem 440

Find the prime factorization of 72. $72 = 2^{3} \cdot 3^{2}$

Find the prime factorization of 150. $150=$ $2 \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 25$ $2^{3} \cdot 3 \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5^{2}$

Find the prime factorization of 120 using exponents for repeats, e.g., $2^{\wedge} 3^{\star} 5$ .

Find the prime factorization of 55 using exponents and * for repeated factors, e.g., $5 * 11$ .

Find the prime factorization of 84 using exponents for repeated factors, like $2^{\wedge} 2^{*} 3$ .

Find the prime factorization of 231 using exponents for repeats and * between factors. Example: $2^{\wedge} 2^{*} 3$ .

Determine the prime factorization of 53. Is it $3^{2} \cdot 5$ , $3^{2} \cdot 17$ , $3^{2} \cdot 7$ , or prime?

Find the prime factorization of 60. Options: $3 \cdot 4 \cdot 5$ , $3^{2} \cdot 7$ , $2^{2} \cdot 3 \cdot 5$ , or 60 is prime.

Write $N=9^{5} \times 15^{5}$ as a product of prime factors in index form.

Find the prime factorization of 93. Format as $a^{b} * c^{d}$ or $a * b * c$ .

Find the prime factorization of 48 in the format $a^{b} * c^{d}$ or $a * b * c$ .

Find the GCF of the numbers $150$ , $275$ , and $420$ .

If 22 divides $n$ , what other natural numbers also divide $n$ ? List them.

Find the prime factorization of these: a. $1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8$ , b. $35^{5} \cdot 65 \cdot 9^{15}$ , c. 181, d. $5000^{9}$ .

Find the prime factorization of these: a. $1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8$ b. $35^{5} \cdot 65 \cdot 9^{15}$ c. 181 d. $5000^{9}$

Identify the group that contains only prime numbers: A. $45,55,65,76$ B. $31,37,61,57$ C. $29,33,73,89$ D. $23,41,53,59$

Find the prime factorization of 210. Options: $6 \cdot 5 - 7$ , $2 \cdot 3 \cdot 35$ , $3 \cdot 7 \cdot 10$ , $2 \cdot 3 \cdot 5 \cdot 7$ .

Find the prime factorization of 144. Options: $2^{3}+3^{4}$ , $2^{2}+3^{5}$ , $2^{4} \cdot 3^{2}$ , $2^{4}+3^{4}$ .

Find the prime factors, LCM, and GCF for 44 and 66. Prime factors: $44=$ , $66=$ , $\mathrm{LCM}=$ .

Selecciona verdadero o falso:
1. La negación de "si los cerdos vuelan, lo creeré" es "si los cerdos no vuelan, no lo creeré".
2. Todos los números enteros son racionales.
3. $3/5$ es irracional.
4. Existe un número que es racional e irracional.

Complete the prime factorization of 180 and express your answer in index form: $180 = 2^a \times 3^b \times 5^c$ .

Find the HCF of 42 and 231 using prime factor trees. Factors: 42 is $2 \times 3 \times 7$ , 231 is $3 \times 7 \times 11$ .

Find the HCF and LCM of $A=2^{6} \times 3^{5} \times 7$ and $B=2^{7} \times 3^{8} \times 5$ in prime factor form.

1. Find the volume of a cube.
2. a. Identify perfect squares from: 16, 125, 20, 144, 25, 225, 100, 10,000. b. Explain your reasoning.
3. a. Identify perfect cubes from: 1, 3, 8, 9, 27, 64, 100, 125.

¿Cuál número tiene como factores primos a $3^{2} \cdot 5$ ? a. 11 b. 30 c. 45 d. 42

¿Cuál es la factorización prima de 24? a. $2 \bullet 3 \bullet 4$ b. $6 \bullet 4$ c. $2^{3} \bullet 3$ d. $2^{2} \cdot 3^{2}$

Encuentra la factorización prima de $120$ . a. $2^{2} \cdot 25 \bullet 4^{2}$ b. $6 \bullet 4 \bullet 5$ c. $2 \cdot 5 \bullet 12$ d. $2^{3} \cdot 3 \cdot 5$

List all factors of 99. Options: $1, 3, 9, 11, 33, 99$ .

Identify the correct prime factorization of 360 in exponential form:
1) $2 \cdot 3^{2} \cdot 5$ 2) $2 \cdot 3 \cdot 5$ 3) $2^{3} \cdot 3^{2} \cdot 5^{2}$ 4) $2^{3} \cdot 3^{2} \cdot 5$

Find the highest common factor (HCF) of 825 and 950 using their prime factor trees: $825 = 3 \times 5^2 \times 11$ , $950 = 2 \times 5^2 \times 19$ .