Question

Find the cube root of 64 by prime factorization method.

Answer 1

Hint: We will use the definition of prime factorization, prime number and prime factors to find the answer. Prime numbers are numbers having only two factors 1 and itself whereas prime factors are factors which are prime. Prime factorization is finding which prime numbers multiply together to make the original number.

Complete step-by-step answer:

Before proceeding with the question, we should understand the concept of prime number and prime factors.

Prime numbers are whole numbers greater than 1, that have only two factors – 1 and the number itself.

A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number. Example: The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers).

Prime factorization is finding which prime numbers multiply together to make the original number.

So here we have to find the cube root of 64 using the prime factorization method.

2	64
2	32
2	16
2	8
2	4
2	2
	1

We see that all the factors are prime factors and \[64=2\times 2\times 2\times 2\times 2\times 2\]. Since 2 occurs in triplets 64 is a perfect cube.
So the cube root of 64 is \[2\times 2=4\].

Note: An alternative method can be by simply finding the factors by breaking the number into smaller numbers and then taking the cube root. We in a hurry can make a mistake by writing one 2 extra or one 2 less and hence we need to be careful while writing the prime factors.