What a Factor Is

Can 54 apples be packed into bags of 6 with none left over? Divide: 54 / 6 is 9, a whole number, so yes, 9 full bags. We say 6 is a factor of 54. A factor of a number divides it with nothing left over.

Now try bags of 4. 54 divided by 4 is 13 with 2 apples left over, so the division does not come out whole, and 4 is not a factor of 54. Every whole number above 1 has at least two factors, 1 and itself, because dividing by either one never leaves anything over.

Factors come with a partner. Since 6 goes into 54 exactly 9 times, 9 is a factor too, and 6 × 9 is 54. Saying 'is a factor of' and 'divides with nothing left over' are the same statement, which is why one division is enough to test a factor.