Question

Check whether 6th can end with the digit0, where 'n' is any natural number​

Answer 1

Answer:

no 6 power n can never end with 0

as the prime factorization of 6 is 2×3

to end with zero the prime factors of a no. should contain one 2 and one 5 as their prime factors

Answer 2

Step-by-step explanation:

We know that,

Every number which ends with zero has its prime factorisation as 2 and 5.

But, prime factorisation of 6 = (2 × 3)

So, 6^n = (2 × 3)^n

But 6 doesn't have 5 as it's prime factor.

According to the Fundamental theorem of Arithmetic,

Every composite number can be expressed as a product of primes, and this factorisation unique, apart form the order in which the prime factors occur.

Therefore, 6 can never have 5 as its prime factor.

Therefore, 6^n never ends with zero.