Question

check whether 4^n can end with the digit '0' for any natural number n.​

Answer 1

Answer:

For unit's digit to be 0, then 4n should have 2 and 5 as its prime factors, but 4n =( 2²)n. it does not contain 5 as one of its prime factors.

hence, 4n will not end with digit 0

Hope you understand

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Answer 2

Answer:

Answer

If the number 4

n

, for any n, were to end with the digit zero, then it should be divisible by 5. That is, prime factorisation of 4

n

would contain the prime factor 5. This is not possible because 4

n

=(2

2

)

n

=2

2n

. So, the only prime in the factorisation of 4

n

is 2.

So, by uniqueness of the fundamental theorem of Arithmetic, there are no other primes in the factorisation of 4

n

.

Hence, there is no natural number 'n' for which 4

n

. ends with the digit zero.