Question

The total number of factors of 21168 is

• A. 24
• B. 48
• C. 60
• D. 80

Answer 1

The correct option is C 60

The prime factorisation of 21168 is $2^4\times 3^3\times 7^2.$

If any natural number N can be written as the product of prime numbers by prime factorisation method

i.e. $N=X^a\times Y^b\times Z^c,$ where X, Y and Z are prime numbers and a, b and c are their respective powers, then, the total number of factors of N is given by (a + 1) (b + 1) (c + 1).

So, the number of factors of 21168 will be (4 + 1) × (3 + 1) × (2 + 1) = 5 × 4 × 3 = 60

Hence, the correct answer is option (c).