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

User Mbm
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1 Answer

4 votes

Answer:

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.

User Stoves
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