Question

What is the smallest natural number n such that n factorial is divisible by 990?

Answer 1

#BAL

That's pretty easy. Consider what the prime factors are that are used to produce 990.

990=2×3×3×5×11

All the factors other than 11 can be found as common factors in factorial less than 11!, but 11 itself only is included in factorials greater than 10!. So n must be 11, and thus n! would be 11!.

I can even tell you quite easily what the result will be after dividing by 990.

990=2×3×3×5×11

2×3×5×11=9×10×11

So 11!=8!×990