How many two digit numbers have exactly 5 divisors.

3
0
5
1
2

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The number of divisors are always in pairs other than for numbers which are in perfect square. Therefore, the number having odd number of divisors could be only perfect squares. Now the possible values are 16, 25, 36, 49, 64, 81.

Now, the square of primes can have only 3 divisors therefore, the remaining numbers are 16, 36, 64, 81.

Now, by checking the number of divisors in these numbers would give us only two values left i.e. 16 & 81