Answer:
The largest n for which [tex]2^{n}[/tex] is a divison of 80 is 4.
Step-by-step 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) [tex]80[/tex] Given
2) [tex]40\times 2[/tex] Definition of multiplication.
3) [tex]20\times 2\times 2[/tex] Definition of multiplication.
4) [tex]10\times 2\times 2\times 2[/tex] Definition of multiplication.
5) [tex]5\times 2\times 2\times 2\times 2[/tex] Definition of multiplication.
6) [tex]5\times 2^{4}[/tex] Definition of power/Result.
In a nutshell, the largest n for which [tex]2^{n}[/tex] is a divison of 80 is 4.
