How many numbers have 6 divisors?

Answer 1

Oh, isn't that a happy little question! Numbers with 6 divisors are special, just like every number is special in its own way. These numbers are known as highly composite numbers, and there are infinitely many of them. So, keep exploring and you'll find more of these unique numbers to brighten your mathematical world.

Answer 2

If you mean have exactly 6 factors then infinitely many!

Including those with at least 6 factors makes no difference, there are still 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:

• has 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 are an infinite number of numbers with exactly 6 factors.