QuestionFind the prime factorization of 225, using exponents for repeated factors.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number225. . Prime factorization means expressing a number as the product of its prime factors.
3. Repeated factors should be written using exponents.

STEP 2

We start the prime factorization by dividing the number by the smallest prime number, which is2. However, since225 is an odd number, it cannot be divided by2. So we move on to the next smallest prime number, which is.

STEP 3

Divide225 by3.
$\frac{225}{3} =75$

STEP 4

We continue the process with the quotient we obtained, which is75. We try to divide75 by3.
$\frac{75}{3} =25$

STEP 5

We continue the process with the quotient we obtained, which is25. Since25 cannot be divided by3, we move on to the next smallest prime number, which is5.

STEP 6

Divide25 by5.
$\frac{25}{5} =5$

STEP 7

We continue the process with the quotient we obtained, which is5. We try to divide5 by5.
$\frac{5}{5} =1$

STEP 8

Once we reach a quotient of1, we stop the process. The prime factors of225 are the divisors we used during this process, which are3,3,5, and5.

STEP 9

Express the prime factorization of225 using exponents for the repeated factors. $225 =3^2 \times5^2$ The prime factorization of225 is $3^2 \times5^2$ .

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QuestionFind the prime factorization of 225, using exponents for repeated factors.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number225. . Prime factorization means expressing a number as the product of its prime factors.
3. Repeated factors should be written using exponents.

STEP 2

We start the prime factorization by dividing the number by the smallest prime number, which is2. However, since225 is an odd number, it cannot be divided by2. So we move on to the next smallest prime number, which is.

STEP 3

Divide225 by3.
$\frac{225}{3} =75$

STEP 4

We continue the process with the quotient we obtained, which is75. We try to divide75 by3.
$\frac{75}{3} =25$

STEP 5

We continue the process with the quotient we obtained, which is25. Since25 cannot be divided by3, we move on to the next smallest prime number, which is5.

STEP 6

Divide25 by5.
$\frac{25}{5} =5$

STEP 7

We continue the process with the quotient we obtained, which is5. We try to divide5 by5.
$\frac{5}{5} =1$

STEP 8

Once we reach a quotient of1, we stop the process. The prime factors of225 are the divisors we used during this process, which are3,3,5, and5.

STEP 9

Express the prime factorization of225 using exponents for the repeated factors. $225 =3^2 \times5^2$ The prime factorization of225 is $3^2 \times5^2$ .

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QuestionFind the prime factorization of 225, using exponents for repeated factors.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of the number225. . Prime factorization means expressing a number as the product of its prime factors.3. Repeated factors should be written using exponents.

STEP 2

We start the prime factorization by dividing the number by the smallest prime number, which is2. However, since225 is an odd number, it cannot be divided by2. So we move on to the next smallest prime number, which is.

STEP 3

Divide225 by3.2253=75\frac{225}{3} =753225​=75

STEP 4

We continue the process with the quotient we obtained, which is75. We try to divide75 by3.753=25\frac{75}{3} =25375​=25

STEP 5

We continue the process with the quotient we obtained, which is25. Since25 cannot be divided by3, we move on to the next smallest prime number, which is5.

STEP 6

Divide25 by5.255=5\frac{25}{5} =5525​=5

STEP 7

We continue the process with the quotient we obtained, which is5. We try to divide5 by5.55=1\frac{5}{5} =155​=1

STEP 8

Once we reach a quotient of1, we stop the process. The prime factors of225 are the divisors we used during this process, which are3,3,5, and5.

STEP 9

Express the prime factorization of225 using exponents for the repeated factors.225=32×52225 =3^2 \times5^2225=32×52The prime factorization of225 is 32×523^2 \times5^232×52.

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Assumptions1. We are asked to find the prime factorization of the number225. . Prime factorization means expressing a number as the product of its prime factors.
3. Repeated factors should be written using exponents.

Divide225 by3.
$\frac{225}{3} =75$

We continue the process with the quotient we obtained, which is75. We try to divide75 by3.
$\frac{75}{3} =25$

Divide25 by5.
$\frac{25}{5} =5$

We continue the process with the quotient we obtained, which is5. We try to divide5 by5.
$\frac{5}{5} =1$

Express the prime factorization of225 using exponents for the repeated factors. $225 =3^2 \times5^2$ The prime factorization of225 is $3^2 \times5^2$ .