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Q.

Find the number of divisors of 5400 which are divisible by 6 but not by 9.

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a

6

b

9

c

12

d

18

answer is B.

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Detailed Solution

5400 = 2^{3} \times 3^{3} \times 5^{2}

Now, the divisors to be the multiple of 6, it has to consist of at least one 2 and one 3 as 6 is made of 6=2×3.
The divisors can’t be multiple of 9 which means it can’t have two or more than two 3s as
9=3×3.
It has to consist of only one 3 and at least one 2.
So, for 2 we have 2+1=3 options and for 5 we have 2+1=3 options.
So, the total number of combinations will be 3×3=9.

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