What is the smallest number with 10 different factors( other than 1)?

This problem is a little tricky. To find the smallest
number that has 10 factors, we need one that can be created by multiplying the smallest
number of prime numbers which are small too.

If a number
has only 2, it has 1 factor. With 2*2, we have 2 factors, with 2*3 we have three factors
2, 3, 6. With 2*2*3, we have 5 factors 2, 3, 4, 6, 12. With 2*2*3*3 we have 8 factors 2,
3, 4, 6, 9, 12, 18, 36. With 2*2*2*3*3 we get 10
factors.

This gives the smallest number with 10 factors as
8*9 = 72. We can verify that 72 has 10 factors which are: 2, 3, 4, 6, 8, 9, 12, 18, 24,
72

The required smallest number with 10
different factors is 72.