Prime Factorization with Exponents - Examples, Exercises and Solutions

What does it mean?

Any natural number that is not prime can be factorized as a product of prime numbers. This process is known as breaking down numbers into prime factors.

From time to time, to solve a certain exercise in a simpler way, we will have to dfactorize the numbers we are given, and rewrite them as products of prime numbers. This factorization gives the possibility to use the numbers in a more comfortable way, for example, by taking advantage of the properties of powers or exponent laws.

For example:
The number 88 can be written as 232^3
The number 11761176 can be also written as 22×3×72 2^2\times3\times7^2

Suggested Topics to Practice in Advance

  1. Prime Numbers and Composite Numbers

Practice Prime Factorization with Exponents

Exercise #1

Write all the factors of the following number: 6 6

Video Solution

Answer

2,3 2,3

Exercise #2

Write all the factors of the following number: 7 7

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Answer

No prime factors

Exercise #3

Write all the factors of the following number: 5 5

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Answer

No prime factors

Exercise #4

Write all the factors of the following number: 9 9

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Answer

3,3 3,3

Exercise #5

Write all the factors of the following number: 8 8

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Answer

2,2,2 2,2,2

Exercise #1

Write all the factors of the following number: 4 4

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Answer

2,2 2,2

Exercise #2

Write all the factors of the following number: 16 16

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Answer

2,2,2,2 2,2,2,2

Exercise #3

Write all the factors of the following number: 12 12

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Answer

3,2,2 3,2,2

Exercise #4

Write all the factors of the following number: 13 13

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Answer

No prime factors

Exercise #5

Write all the factors of the following number: 14 14

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Answer

2,7 2,7

Exercise #1

Write all the factors of the following number: 18 18

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Answer

2,3,3 2,3,3

Exercise #2

Write all the factors of the following number: 26 26

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Answer

13,2 13,2

Exercise #3

Write all the factors of the following number: 31 31

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Answer

No prime factors

Exercise #4

Write all the factors of the following number: 99 99

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Answer

11,3,3 11,3,3

Exercise #5

Write all the factors of the following number: 290 290

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Answer

5,2,29 5,2,29

Topics learned in later sections

  1. Prime Factorization
  2. Divisibility Rules for 2, 4, and 10
  3. Divisibility Rules for 3, 6, and 9