Question

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

Answer 1

21600 = 25 x 33 x 52 if a number is divisible by 10 but not by 15, then it will be divisible by 2 and 5 but not by 3.

  All such divisors will have the form: 2x 5y where x Î {1, 2, 3, 4, 5} and y Î {1, 2}.

 So, the divisors are: 2151, 2152, 2251, 2252, ……….2551, 2552. .

 These ten numbers are divisible by 2 and 5 but not by 3 and will be a positive integer divisor of 25 x 33 x 52.

 So, 10 divisors of 21600 are divisible by 10 but not by 15.

Answer 2

Answer:10

Explanation: see we want no. divisible by 10 but not by 15

First prime factorise 2^5*5^2*3^3 =21600

For no. to be not be divisible by 15 we should not take therefore

No. Of ways of taking 2s and 5s from 5 2s and 2 5s = 5*2 (we are excluding the case of not taking any no )

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