QuestionFind the prime factorization of 36, using exponents for repeated factors. What is it?

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number36. . Prime factorization means expressing the number as a product of prime numbers.
3. Repeated factors should be written using exponents.

STEP 2

We start by finding the smallest prime number that divides36. The smallest prime number is2, and it does divide36.
$36 \div2 =18$

STEP 3

We continue this process with the quotient we just found,18. The smallest prime number that divides18 is2.
$18 \div2 =9$

STEP 4

We continue this process with the quotient we just found,9. The smallest prime number that divides9 is3.
$9 \div3 =3$

STEP 5

We continue this process with the quotient we just found,3. The smallest prime number that divides3 is3.
$3 \div3 =1$

STEP 6

We stop this process when we reach the number1. Now, we can write36 as a product of the prime numbers we found during this process.
$36 =2 \times2 \times3 \times3$

STEP 7

We can write the repeated factors using exponents.
$36 =2^2 \times3^2$ The prime factorization of36 is $2^2 \times3^2$ .

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QuestionFind the prime factorization of 36, using exponents for repeated factors. What is it?

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number36. . Prime factorization means expressing the number as a product of prime numbers.
3. Repeated factors should be written using exponents.

STEP 2

We start by finding the smallest prime number that divides36. The smallest prime number is2, and it does divide36.
$36 \div2 =18$

STEP 3

We continue this process with the quotient we just found,18. The smallest prime number that divides18 is2.
$18 \div2 =9$

STEP 4

We continue this process with the quotient we just found,9. The smallest prime number that divides9 is3.
$9 \div3 =3$

STEP 5

We continue this process with the quotient we just found,3. The smallest prime number that divides3 is3.
$3 \div3 =1$

STEP 6

We stop this process when we reach the number1. Now, we can write36 as a product of the prime numbers we found during this process.
$36 =2 \times2 \times3 \times3$

STEP 7

We can write the repeated factors using exponents.
$36 =2^2 \times3^2$ The prime factorization of36 is $2^2 \times3^2$ .

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QuestionFind the prime factorization of 36, using exponents for repeated factors. What is it?

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number36. . Prime factorization means expressing the number as a product of prime numbers.3. Repeated factors should be written using exponents.

STEP 2

We start by finding the smallest prime number that divides36. The smallest prime number is2, and it does divide36.36÷2=1836 \div2 =1836÷2=18

STEP 3

We continue this process with the quotient we just found,18. The smallest prime number that divides18 is2.18÷2=918 \div2 =918÷2=9

STEP 4

We continue this process with the quotient we just found,9. The smallest prime number that divides9 is3.9÷3=39 \div3 =39÷3=3

STEP 5

We continue this process with the quotient we just found,3. The smallest prime number that divides3 is3.3÷3=13 \div3 =13÷3=1

STEP 6

We stop this process when we reach the number1. Now, we can write36 as a product of the prime numbers we found during this process.36=2×2×3×336 =2 \times2 \times3 \times336=2×2×3×3

STEP 7

We can write the repeated factors using exponents.36=22×3236 =2^2 \times3^236=22×32The prime factorization of36 is 22×322^2 \times3^222×32.

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Assumptions1. We are asked to find the prime factorization of the number36. . Prime factorization means expressing the number as a product of prime numbers.
3. Repeated factors should be written using exponents.

We start by finding the smallest prime number that divides36. The smallest prime number is2, and it does divide36.
$36 \div2 =18$

We continue this process with the quotient we just found,18. The smallest prime number that divides18 is2.
$18 \div2 =9$

We continue this process with the quotient we just found,9. The smallest prime number that divides9 is3.
$9 \div3 =3$

We continue this process with the quotient we just found,3. The smallest prime number that divides3 is3.
$3 \div3 =1$

We stop this process when we reach the number1. Now, we can write36 as a product of the prime numbers we found during this process.
$36 =2 \times2 \times3 \times3$

We can write the repeated factors using exponents.
$36 =2^2 \times3^2$ The prime factorization of36 is $2^2 \times3^2$ .