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Home >> Cube Root >> Cube Root by Prime Factorization Method >>

Cube Root by Prime Factorization Method

Cube Root by Prime Factorization Method Cube Root by Shortcut Method

Before you study How to calculate Cube Root by Prime Factorization Method, you are adviced to read:

What are Cube Numbers ?
What is a Cube Root ?
What is Prime Factorization ?

Steps of finding Cube root by prime factorization method:

Step 1: Find Prime Factorization of given number
Step 2: Make one group of three same prime factors
Step 3: Collect one prime factor from each group
Step 4: Multiply the collected prime factors ( if only one pair, ignore this step)
Step 5: Resultant number is the cube root of the given number

Example 1: Find cube root of 8 using prime factorization method.
Solution: Steps are as follows:

Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 8 = 2 X 2 X 2

Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2

Step 3: Collect one prime factor from each group
= 2

Step 5: Resultant number is the cube root of the given number and we get:
2 is the cube root of 8

Or we can write it as:
  8   = 2



Example 2: Find cube root of 216 using prime factorization method.
Solution: Steps are as follows:

Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 216 = 2 X 2 X 2 X 3 X 3 X 3

Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 3 X 3 X 3

Step 3: Collect one prime factor from each group
= 2 X 3

Step 4: Multiply the collected prime factors and we get:
= 6

Step 5: Resultant number is the cube root of the given number
6 is the cube root of 216

Or we can write it as:
  216   = 6



Example 3: Find cube root of 1000 using prime factorization method.
Solution: Steps are as follows:

Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 1000 = 2 X 2 X 2 X 5 X 5 X 5

Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 5 X 5 X 5

Step 3: Collect one prime factor from each group
= 2 X 5

Step 4: Multiply the collected prime factors and we get:
= 10

Step 5: Resultant number is the cube root of the given number
10 is the cube root of 1000

Or we can write it as:
  1000   = 10



Example 4: Find cube root of 74088 using prime factorization method.
Solution: Steps are as follows:

Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 74088 = 2 X 2 X 2 X 3 X 3 X 3 X 7 X 7 X 7

Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 3 X 3 X 3 X 7 X 7 X 7

Step 3: Collect one prime factor from each group
= 2 X 3 X 7

Step 4: Multiply the collected prime factors and we get:
= 42

Step 5: Resultant number is the cube root of the given number
42 is the cube root of 74088

Or we can write it as:
  74088   = 42

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