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There are infinitely many!

The number of factors of a number depends solely upon the prime factorisation of the number. There will be exactly 6 factors if the number:

  • is a single prime to the power five (eg 32 = 2 x 2 x 2 x 2 x 2 = 25); or
  • is the product of two primes, one of which is squared (eg 12 = 2 x 2 x 3 = 22 x 3; 50 = 2 x 5 x 5 = 2 x 52)

As there is an infinite number of primes, there is an infinite number of numbers with exactly 6 factors.

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63 isn't a factor of 6

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Q: How many numbers have 6 factors?
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