Solved on Nov 15, 2023

Find the prime factorization of 125. $5 \times 5 \times 5$ , $5 \times 25$ , or $5 \times 100$ .

STEP 1

Assumptions1. The number for which we need to find the prime factorization is125

STEP 2

Prime factorization is the process of determining the prime numbers that multiply together to make a certain number. A prime number is a number greater than1 that has no positive divisors other than1 and itself.

STEP 3

We start by dividing the number by the smallest prime number, which is2. If it's not divisible by2, we move to the next prime number, which is3. In this case,125 is not divisible by2, so we move to the next prime number, which is3. It's also not divisible by3, so we move to the next prime number, which is5.

STEP 4

125 is divisible by. So, we divide125 by.
$125 / =25$

STEP 5

We continue this process with the quotient we just found, which is25.25 is not divisible by2 or3, but it is divisible by5.
$25 /5 =5$

STEP 6

We continue this process with the quotient we just found, which is5.5 is not divisible by2,3, or4, but it is divisible by5.
$5 /5 =1$

STEP 7

When we reach1, we stop, as1 is not a prime number. The prime factorization of125 is therefore $5 \times5 \times5$ .
The correct answer is $5 \times5 \times5$ .

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Find the prime factorization of 125. $5 \times 5 \times 5$ , $5 \times 25$ , or $5 \times 100$ .

STEP 1

Assumptions1. The number for which we need to find the prime factorization is125

STEP 2

Prime factorization is the process of determining the prime numbers that multiply together to make a certain number. A prime number is a number greater than1 that has no positive divisors other than1 and itself.

STEP 3

STEP 4

125 is divisible by. So, we divide125 by.
$125 / =25$

STEP 5

We continue this process with the quotient we just found, which is25.25 is not divisible by2 or3, but it is divisible by5.
$25 /5 =5$

STEP 6

We continue this process with the quotient we just found, which is5.5 is not divisible by2,3, or4, but it is divisible by5.
$5 /5 =1$

STEP 7

When we reach1, we stop, as1 is not a prime number. The prime factorization of125 is therefore $5 \times5 \times5$ .
The correct answer is $5 \times5 \times5$ .

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Find the prime factorization of 125. 5×5×55 \times 5 \times 55×5×5, 5×255 \times 255×25, or 5×1005 \times 1005×100.

STEP 1

Assumptions1. The number for which we need to find the prime factorization is125

STEP 2

Prime factorization is the process of determining the prime numbers that multiply together to make a certain number. A prime number is a number greater than1 that has no positive divisors other than1 and itself.

STEP 3

STEP 4

125 is divisible by. So, we divide125 by.125/=25125 / =25125/=25

STEP 5

We continue this process with the quotient we just found, which is25.25 is not divisible by2 or3, but it is divisible by5.25/5=525 /5 =525/5=5

STEP 6

We continue this process with the quotient we just found, which is5.5 is not divisible by2,3, or4, but it is divisible by5.5/5=15 /5 =15/5=1

STEP 7

When we reach1, we stop, as1 is not a prime number. The prime factorization of125 is therefore 5×5×55 \times5 \times55×5×5.The correct answer is 5×5×55 \times5 \times55×5×5.

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Find the prime factorization of 125. $5 \times 5 \times 5$ , $5 \times 25$ , or $5 \times 100$ .

125 is divisible by. So, we divide125 by.
$125 / =25$

We continue this process with the quotient we just found, which is25.25 is not divisible by2 or3, but it is divisible by5.
$25 /5 =5$

We continue this process with the quotient we just found, which is5.5 is not divisible by2,3, or4, but it is divisible by5.
$5 /5 =1$

When we reach1, we stop, as1 is not a prime number. The prime factorization of125 is therefore $5 \times5 \times5$ .
The correct answer is $5 \times5 \times5$ .