Question

2 × 2 × are the prime factors of 108.

• A. $3\times 3\times 3$
• B. $3\times 3\times 2$
• C. $3\times 4\times 3$

Answer 1

The correct option is A $3\times 3\times 3$

Factors of 108 by prime factorization method:

Step 1: Write the pair of factors, which on multiplication gives the required number.
108 = 2 × 54

Step 2: See the factors, whether each one of them is prime or not.

54 is not a prime number and can be dissociated as a product of 2 by 27.
27 is not a prime number and can be dissociated as a product of 3 by 9 and 9 can be dissociated as 3 × 3.

Step 3: As per the criteria, 108 can be written as
108 = 2 × 54
= 2 × 2 × 27
=2 × 2 × 3 × 9
= 2 × 2 × 3 × 3 × 3.
So, prime factorization of 108
= 2 × 2 × 3 × 3 × 3.