Question

Compute the largest n for which 2^n is a divisor of 80!

Answer 1

The largest n for which
`2^(n)` is a divison of 80 is 4.

Explanation:

Numbers can be composited, that is, a product of prime numbers, or primer numbers themselves. A entire number is a divisor of another entire number if result is an entire number.

As first step we need to decompose 80 as a product of prime numbers, whose procedure is presented below:

1)
`80` Given

2)
`40* 2` Definition of multiplication.

3)
`20* 2* 2` Definition of multiplication.

4)
`10* 2* 2* 2` Definition of multiplication.

5)
`5* 2* 2* 2* 2` Definition of multiplication.

6)
`5* 2^(4)` Definition of power/Result.

In a nutshell, the largest n for which
`2^(n)` is a divison of 80 is 4.