1 as prime factor

[vanesslondon]

I am confused: in some questions 1 seems to count as a prime factor and in others it doesn't. When does it count as a prime factor and when doesn't it count please?
Thanks!

[Ian Stewart]

1 is not a prime number, so it should never be counted as a prime factor. It is, however, a factor of every positive integer, so it should always be counted as a factor. It's possible you've seen two different questions, one which asked:

"How many prime factors does 45 have?" (the answer is two: 3 and 5)

and one which asked

"How many positive factors does 45 have?" (the answer is six: 1, 3, 5, 9, 15, 45).

In the first case, you would definitely not count 1; in the second case you would definitely need to count 1.

[vanesslondon]

Thanks so much, that's great.