Prime Factorization and Exponents

Prime Factorization

​How to find the prime factorization of any number

Step 1: Find two factors for the number.

​24

​Step 2: If a factor is a prime factor, leave it there. If a factor is a composite factor, factor that again.

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​8

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​3

​Step 3: Repeat steps 1 and 2 until all factors are prime numbers.

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​_

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​2

​4

​3

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​_

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​2

​2

​2

​3

Once you have all of the factors prime, you found the prime factorization!

​The prime factorization of 24 is:

​(The factors can be rearranged in a different prime factorization of the same number.)

​The prime factorization does not have to be in expanded form. The prime factorization can have exponents in that expression, based on how many prime factors are there.

​

​For example:

​The expression in exponential form still represents the prime factorization of 24.

Multiple Choice

Express 5  $$\times$$  5  $$\times$$  5  $$\times$$  7 in exponential form.

• 7³  $$\times$$  5

• 5³  $$\times$$  7

• 5⁷  $$\times$$  3

Multiple Choice

Express 3  $$\times$$  7  $$\times$$  7  $$\times$$  3  $$\times$$  7 in exponential form.

• 3²  $$\times$$  7³

• 7²  $$\times$$  3³

• 3⁷  $$\times$$  2³

Multiple Choice

Find the prime factorization of 54. Decompose 54 into 9 $$\times$$  6 first.

• 2⁴  $$\times$$  3

• 2 $$\times$$  3³

• 2²  $$\times$$  3²

Multiple Choice

Find the prime factorization of 80. Decompose 80 into 10  $$\times$$  8 first.

• 2⁵  $$\times$$  4

• 4⁵  $$\times$$  2

• 2⁴  $$\times$$  5

Multiple Choice

Find the prime factorization of 75. Decompose 75 into 15  $$\times$$  5 first.

• 3  $$\times$$  5²

• 5³  $$\times$$  2

• 2  $$\times$$  3⁵

Multiple Choice

Find the prime factorization of 36. Decompose 36 into 9  $$\times$$  4 first.

• 22 $$\times$$  2³

• 3⁴ $$\times$$  2

• 2² $$\times$$  3²

Multiple Choice

Find the prime factorization of 78. Decompose 78 into 13  $$\times$$  6 first.

• 13  $$\times$$  2³

• 2  $$\times$$  3¹³

• 2  $$\times$$  3  $$\times$$  13

Multiple Choice

Find the prime factorization of 720. Decompose 720 into 40 $$\times$$  18 first.

• 2⁴  $$\times$$  3²  $$\times$$  5

• 24  $$\times$$  32

• 3⁵  $$\times$$  4³

Multiple Choice

Find the prime factorization of 576. Decompose 576 into 24  $$\times$$  24 first.

• 3⁴  $$\times$$  5

• 3⁶  $$\times$$  2²

• 2⁶  $$\times$$  3²

Multiple Choice

Find the prime factorization of 504. Decompose 504 to 24  $$\times$$  21 first.

• 2⁵  $$\times$$  3⁷

• 2³  $$\times$$  3²  $$\times$$  7

• 3³  $$\times$$  2²  $$\times$$  5

Multiple Choice

Solve for y to complete this prime factorization:

y  $$\times$$  3²  $$=$$  72

• 2³

• 2²

• 3²

Multiple Choice

Solve for y to complete this prime factorization:

2⁴  $$\times$$  y  $$=$$  80

• 2

• 5

• 3²

Multiple Choice

Solve for y to complete this prime factorization:

2  $$\times$$  y  $$\times$$  7  $$=$$  42

• 5

• 2

• 3

Multiple Choice

Solve for y to complete this prime factorization:

2³  $$\times$$  y  $$=$$  72

• 2²

• 2³

• 3²

Multiple Choice

Solve for y to complete this prime factorization:

y  $$\times$$  5  $$=$$  135

• 2²

• 3

• 3³

Multiple Choice

Solve for y to complete this prime factorization:

2⁵  $$\times$$  y  $$=$$  224

• 3²

• 7

• 2³

Multiple Choice

Solve for y to complete this prime factorization:

2⁴  $$\times$$  3²  $$\times$$  y  $$=$$  720

• 3

• 7

• 5