#1**0 **

20! + 12! = 12!(x + 1). Since we know that x is an even number, (x + 1) is an odd number, and therefore cannot "produce" any more factors of 12.

Therefore, the largest integer n for which 12^n divides it would be how much 12^n divides 12!.

12 = 2^2 * 3

We have to see how many factors of 2 are there in 12!, divide that by 2 and set that equal to y.

In addition, we can see how many factors of 3 there are in 12! and set that equal to z.

1: 2, 4, 6, 8, 10, 12

2: 4, 8, 12

3: 8

Adding up gives us: 10

Therefore, there are 5 2^2 terms.

1: 3, 6, 9, 12

2: 9

There are also 5 factors of 3 in the expression.

Therefore, 5 is the largest integer for n that divides 20! + 12!

Voldemort Jul 22, 2022