Question

if the number 4th isend with the digit 6,nEN, then the value of n is​

Answer 1

Answer:

For the number 4

n

to end with digit zero for any natural number n, it should be divisible by 5. This means that the prime factorisation of 4

n

should contain the prime number 5.But it is not possible because 4

n

=(2)

2n

so 2 is the only prime in the factorisation of 4

n

. Since 5 is not present in the prime factorization, so there is no natural number n for which 4

n

ends with the digit zero.

Answer 2

Concept

A process of factoring a number in terms of prime numbers that means the factors will be prime numbers is called as prime factorization.

Given

4ⁿ ends with 6

Find

The value of n

Solution

4ⁿ= (2 * 2)ⁿ

4ⁿ= 2ⁿ * 2ⁿ

As 2 is a factor of 4ⁿ

Hence 4ⁿ is always a even number and ends with 4 and 6

So for any value of n = 2,4,6,8,10...  4ⁿ ends with 6.

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