What number has 9 factors?

Answer 1

36 and 100, among others.

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To have an odd number of factors, one of them must be repeated, which means the number must be a perfect square.

In the prime factorisation of a perfect square in power format, every power of a prime is an even number.

To find the number of factors of a number, add one to the powers of all the primes in the number's prime factorisation and multiply them together.

Thus all numbers of the form p^8 or p²q² where p and q are different primes have 9 factors.

so 2^8 = 256, 3^8 = 6561, 5^8 = 390625, ... all have 9 factors, as do:

2²3² = 36, 2²5² = 100, 2²7² = 196, 3²5² = 225, 3²,7² = 441, ...