Examine whether $(7)^n$ can end with the digit 5 for any $n\in N$.

Given :

The given number term is $7^n$.

To do :

We have to check  whether $(7)^n$ can end with the digit 5 for any $n\in N$.

Solution :

If a number ends with the digit 5, it should have 5 as it's prime factor.

$7^n$

$7 = 1\times 7$

$7^n= (1\times 7)^n$

The number 7 has 1 and 7 as it's prime factors but not 5.

Therefore, it can be concluded that $(7)^n$ cannot end with the digit 5 for any $n\in N$

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Updated on: 10-Oct-2022

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