Prime Factorization with Exponents - Examples, Exercises and Solutions

Question Types:
Prime Factorization: Recognizing divisibility rulesPrime Factorization: Using factors to solvePrime Factorization: Identify the factors of

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

Detailed explanation

Suggested Topics to Practice in Advance

  1. Prime Numbers and Composite Numbers

Practice Prime Factorization with Exponents

Question 1

Write all the factors of the following number: \( 4 \)

Question 2

Write all the factors of the following number: \( 5 \)

Question 3

Write all the factors of the following number: \( 6 \)

Question 4

Write all the factors of the following number: \( 7 \)

Question 5

Write all the factors of the following number: \( 8 \)

Examples with solutions for Prime Factorization with Exponents

Exercise #1

Write all the factors of the following number: 4 4

Video Solution

Answer

2,2 2,2

Exercise #2

Write all the factors of the following number: 5 5

Video Solution

Answer

No prime factors

Exercise #3

Write all the factors of the following number: 6 6

Video Solution

Answer

2,3 2,3

Exercise #4

Write all the factors of the following number: 7 7

Video Solution

Answer

No prime factors

Exercise #5

Write all the factors of the following number: 8 8

Video Solution

Answer

2,2,2 2,2,2

Question 1

Write all the factors of the following number: \( 9 \)

Question 2

Write all the factors of the following number: \( 12 \)

Question 3

Write all the factors of the following number: \( 13 \)

Question 4

Write all the factors of the following number: \( 14 \)

Question 5

Write all the factors of the following number: \( 16 \)

Exercise #6

Write all the factors of the following number: 9 9

Video Solution

Answer

3,3 3,3

Exercise #7

Write all the factors of the following number: 12 12

Video Solution

Answer

3,2,2 3,2,2

Exercise #8

Write all the factors of the following number: 13 13

Video Solution

Answer

No prime factors

Exercise #9

Write all the factors of the following number: 14 14

Video Solution

Answer

2,7 2,7

Exercise #10

Write all the factors of the following number: 16 16

Video Solution

Answer

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

Question 1

Write all the factors of the following number: \( 18 \)

Question 2

Write all the factors of the following number: \( 26 \)

Question 3

Write all the factors of the following number: \( 290 \)

Question 4

Write all the factors of the following number: \( 31 \)

Question 5

Write all the factors of the following number: \( 500 \)

Exercise #11

Write all the factors of the following number: 18 18

Video Solution

Answer

2,3,3 2,3,3

Exercise #12

Write all the factors of the following number: 26 26

Video Solution

Answer

13,2 13,2

Exercise #13

Write all the factors of the following number: 290 290

Video Solution

Answer

5,2,29 5,2,29

Exercise #14

Write all the factors of the following number: 31 31

Video Solution

Answer

No prime factors

Exercise #15

Write all the factors of the following number: 500 500

Video Solution

Answer

5,5,5,2,2 5,5,5,2,2

Topics learned in later sections

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