QuestionFind the prime factorization of 100. Options: A. $2 \times 2 \times 5 \times 5$ , B. $2 \times 5$ , C. $2 \times 2 \times 5$ , D. $10 \times 10$

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of100. . Prime factorization of a number is the expression of that number as a product of prime numbers.

STEP 2

We start by finding the smallest prime number that divides100. The smallest prime number is2, and it does divide100.
$100 /2 =50$

STEP 3

We continue this process with the quotient we just found,50. The smallest prime number that divides50 is also2.
$50 /2 =25$

STEP 4

We continue this process with the quotient we just found,25. The smallest prime number that divides25 is.
$25 / =$

STEP 5

We continue this process with the quotient we just found,5. The smallest prime number that divides5 is5.
$5 /5 =1$

STEP 6

Now that our quotient is1, we have found all the prime factors of100. They are2,2,5, and5.
$100 =2 \times2 \times5 \times5$ So, the prime factorization of100 is $2 \times2 \times5 \times5$ . Therefore, the correct answer is option A.

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QuestionFind the prime factorization of 100. Options: A. $2 \times 2 \times 5 \times 5$ , B. $2 \times 5$ , C. $2 \times 2 \times 5$ , D. $10 \times 10$

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of100. . Prime factorization of a number is the expression of that number as a product of prime numbers.

STEP 2

We start by finding the smallest prime number that divides100. The smallest prime number is2, and it does divide100.
$100 /2 =50$

STEP 3

We continue this process with the quotient we just found,50. The smallest prime number that divides50 is also2.
$50 /2 =25$

STEP 4

We continue this process with the quotient we just found,25. The smallest prime number that divides25 is.
$25 / =$

STEP 5

We continue this process with the quotient we just found,5. The smallest prime number that divides5 is5.
$5 /5 =1$

STEP 6

Now that our quotient is1, we have found all the prime factors of100. They are2,2,5, and5.
$100 =2 \times2 \times5 \times5$ So, the prime factorization of100 is $2 \times2 \times5 \times5$ . Therefore, the correct answer is option A.

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QuestionFind the prime factorization of 100. Options: A. 2×2×5×52 \times 2 \times 5 \times 52×2×5×5, B. 2×52 \times 52×5, C. 2×2×52 \times 2 \times 52×2×5, D. 10×1010 \times 1010×10

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of100. . Prime factorization of a number is the expression of that number as a product of prime numbers.

STEP 2

We start by finding the smallest prime number that divides100. The smallest prime number is2, and it does divide100.100/2=50100 /2 =50100/2=50

STEP 3

We continue this process with the quotient we just found,50. The smallest prime number that divides50 is also2.50/2=2550 /2 =2550/2=25

STEP 4

We continue this process with the quotient we just found,25. The smallest prime number that divides25 is.25/=25 / =25/=

STEP 5

We continue this process with the quotient we just found,5. The smallest prime number that divides5 is5.5/5=15 /5 =15/5=1

STEP 6

Now that our quotient is1, we have found all the prime factors of100. They are2,2,5, and5.100=2×2×5×5100 =2 \times2 \times5 \times5100=2×2×5×5So, the prime factorization of100 is 2×2×5×52 \times2 \times5 \times52×2×5×5. Therefore, the correct answer is option A.

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QuestionFind the prime factorization of 100. Options: A. $2 \times 2 \times 5 \times 5$ , B. $2 \times 5$ , C. $2 \times 2 \times 5$ , D. $10 \times 10$

We start by finding the smallest prime number that divides100. The smallest prime number is2, and it does divide100.
$100 /2 =50$

We continue this process with the quotient we just found,50. The smallest prime number that divides50 is also2.
$50 /2 =25$

We continue this process with the quotient we just found,25. The smallest prime number that divides25 is.
$25 / =$

We continue this process with the quotient we just found,5. The smallest prime number that divides5 is5.
$5 /5 =1$

Now that our quotient is1, we have found all the prime factors of100. They are2,2,5, and5.
$100 =2 \times2 \times5 \times5$ So, the prime factorization of100 is $2 \times2 \times5 \times5$ . Therefore, the correct answer is option A.