Solved on Jan 22, 2024

Find the prime factorization of 124.

STEP 1

Assumptions
1. We need to express the number 124 as a product of its prime factors.
2. A prime factor of a number is a prime number that divides the number exactly without leaving a remainder.
3. The process of finding prime factors is known as prime factorization.

STEP 2

Begin the prime factorization by finding the smallest prime number that divides 124 exactly.

STEP 3

Check if 124 is divisible by 2, which is the smallest prime number.
$124 \mod 2 = 0$

STEP 4

Since 124 is divisible by 2, divide 124 by 2 to find the quotient.
$\frac{124}{2} = 62$

STEP 5

Write down 2 as one of the prime factors and continue the factorization process with the quotient, which is 62.

STEP 6

Check if 62 is divisible by 2.
$62 \mod 2 = 0$

STEP 7

Since 62 is divisible by 2, divide 62 by 2 to find the next quotient.
$\frac{62}{2} = 31$

STEP 8

Write down another 2 as one of the prime factors and continue the factorization process with the quotient, which is 31.

STEP 9

Determine if 31 is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

STEP 10

Since 31 cannot be divided exactly by any prime number smaller than itself, it is a prime number.

STEP 11

Write down 31 as the last prime factor.

STEP 12

Combine all the prime factors obtained to express 124 as a product of its prime factors.
$124 = 2 \times 2 \times 31$

STEP 13

Write the prime factorization using exponents for any repeated factors.
$124 = 2^2 \times 31$
The prime factorization of 124 is $2^2 \times 31$ .

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Find the prime factorization of 124.

STEP 1

Assumptions
1. We need to express the number 124 as a product of its prime factors.
2. A prime factor of a number is a prime number that divides the number exactly without leaving a remainder.
3. The process of finding prime factors is known as prime factorization.

STEP 2

Begin the prime factorization by finding the smallest prime number that divides 124 exactly.

STEP 3

Check if 124 is divisible by 2, which is the smallest prime number.
$124 \mod 2 = 0$

STEP 4

Since 124 is divisible by 2, divide 124 by 2 to find the quotient.
$\frac{124}{2} = 62$

STEP 5

Write down 2 as one of the prime factors and continue the factorization process with the quotient, which is 62.

STEP 6

Check if 62 is divisible by 2.
$62 \mod 2 = 0$

STEP 7

Since 62 is divisible by 2, divide 62 by 2 to find the next quotient.
$\frac{62}{2} = 31$

STEP 8

Write down another 2 as one of the prime factors and continue the factorization process with the quotient, which is 31.

STEP 9

Determine if 31 is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

STEP 10

Since 31 cannot be divided exactly by any prime number smaller than itself, it is a prime number.

STEP 11

Write down 31 as the last prime factor.

STEP 12

Combine all the prime factors obtained to express 124 as a product of its prime factors.
$124 = 2 \times 2 \times 31$

STEP 13

Write the prime factorization using exponents for any repeated factors.
$124 = 2^2 \times 31$
The prime factorization of 124 is $2^2 \times 31$ .

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Find the prime factorization of 124.

STEP 1

Assumptions1. We need to express the number 124 as a product of its prime factors.2. A prime factor of a number is a prime number that divides the number exactly without leaving a remainder.3. The process of finding prime factors is known as prime factorization.

STEP 2

Begin the prime factorization by finding the smallest prime number that divides 124 exactly.

STEP 3

Check if 124 is divisible by 2, which is the smallest prime number.124mod 2=0124 \mod 2 = 0124mod2=0

STEP 4

Since 124 is divisible by 2, divide 124 by 2 to find the quotient.1242=62\frac{124}{2} = 622124​=62

STEP 5

Write down 2 as one of the prime factors and continue the factorization process with the quotient, which is 62.

STEP 6

Check if 62 is divisible by 2.62mod 2=062 \mod 2 = 062mod2=0

STEP 7

Since 62 is divisible by 2, divide 62 by 2 to find the next quotient.622=31\frac{62}{2} = 31262​=31

STEP 8

Write down another 2 as one of the prime factors and continue the factorization process with the quotient, which is 31.

STEP 9

Determine if 31 is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

STEP 10

Since 31 cannot be divided exactly by any prime number smaller than itself, it is a prime number.

STEP 11

Write down 31 as the last prime factor.

STEP 12

Combine all the prime factors obtained to express 124 as a product of its prime factors.124=2×2×31124 = 2 \times 2 \times 31124=2×2×31

STEP 13

Write the prime factorization using exponents for any repeated factors.124=22×31124 = 2^2 \times 31124=22×31The prime factorization of 124 is 22×312^2 \times 3122×31.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. We need to express the number 124 as a product of its prime factors.
2. A prime factor of a number is a prime number that divides the number exactly without leaving a remainder.
3. The process of finding prime factors is known as prime factorization.

Check if 124 is divisible by 2, which is the smallest prime number.
$124 \mod 2 = 0$

Since 124 is divisible by 2, divide 124 by 2 to find the quotient.
$\frac{124}{2} = 62$

Check if 62 is divisible by 2.
$62 \mod 2 = 0$

Since 62 is divisible by 2, divide 62 by 2 to find the next quotient.
$\frac{62}{2} = 31$

Combine all the prime factors obtained to express 124 as a product of its prime factors.
$124 = 2 \times 2 \times 31$

Write the prime factorization using exponents for any repeated factors.
$124 = 2^2 \times 31$
The prime factorization of 124 is $2^2 \times 31$ .