Question

Check whether (28)n can end with the digit 0 for any natural number n

Answer 1

Chapter 1 Real Numbers

Class 10

To find whether any digit of 28ⁿ ends with zero.

Factorizing 28ⁿ,

28ⁿ

=(2×2×7)ⁿ

=(2²×7)ⁿ

=2²ⁿ×7ⁿ

As the prime factorization of 28ⁿ,has no 5 in its factorization.

Implies,28ⁿ can't end with zero for any value of n.

Some important concepts:

Euclid's Division Lemma,

There exist two non negative integers a and b such that q and r satisfy the equation:

→a=bq+r

Fundamental Theorm of Arithmetic,

Every number can be expressed as a product of prime numbers,here the numbers placed are not important

Answer 2

$\large{\underline{\boxed{\tt Answer}}}$

28ⁿ cannot end with the digit 0 for any natural number n.  

$\large{\underline{\boxed{\tt Step-by-step\ Explanation}}}$

Given Problem:

Check whether (28)ⁿ can end with the digit 0 for any natural number n

Solution:

To Do:

Check Whether (28)ⁿ can end with the digit 0 for any natural number n

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Method:

First, we have factorize 28ⁿ

Factorizing,

$(2*2*7)^n$

$(2^2*7)^n$

$2^2^n*7^n$

After Factorizing,

It can be abserve that for any value of n, 28n will not be divisible by 5.

Therefore,

28n cannot end with the digit 0 for any natural number n.