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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE