Question

determine the HCF of 48, 64 by prime factorization method​

Answer 1

Prime Factorization is a method where the number is expressed as a product of it's primes and the common terms are it's HCF

$\textsf{HCF(48,64)}$

48 = 2×2×2×2×3

64 = 2×2×2×2×2×2

Common terms - 2×2×2×2 = 16

HCF - 16

Answer 2

Given:  

Two numbers 48, and 64.

To Find:

The HCF of the two numbers using the prime factorization method is?

Solution:                      

1. The two given numbers are 48 and 64.

2. Factorize the two given numbers as the product of prime factors,

=> 48 = 2 x 24,

=> 48 = 2 x 2 x 12,

=> 48 = 2 x 2 x 2 x 6,

=> 48 = 2 x 2 x 2 x 2 x 3.

=> 64 = 2 x 32,

=> 64 = 2 x 2 x 16,

=> 64 = 2 x 2 x 2 x 8,

=> 64 = 2 x 2 x 2 x 2 x 4,

=> 64 = 2 x 2 x 2 x 2 x 2 x 2,

3. Find the total number of common terms in the two prime factors,

=> The number 2 is repeated 4 times commonly for the two numbers,

=> The HCF of the two numbers is 2 x 2 x 2 x 2 = 16.

Therefore, the HCF of 48, 64 is 16.