How many divisors of 21600 are divisible by 10 but not by 1…

Maths Permutations & Combination Problem Based on Distinct and Identical Objects and Divisors Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

How many divisors of 21600 are divisible by 10 but not by 15?

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Text Solution

Verified by Experts

The correct answer is:

Here 21600 = 2 5 . 3 3 . 5 2 ⇒ (2 × 5) × 2 4 × 3 3 × 5 1

Now numbers which are divisible by 10 = (4 + 1)(3 + 1)(1 + 1) = 40

(2 × 3 × 5) × (2 4 × 3 2 × 51) now numbers which are divisible by both 10 and 15

= (4 +1)(2 +1)(1+1) = 30

So the numbers which are divisible by only 40 – 30 = 10

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