Question

Prove that n is a natural number then 12th no. End with 0and5

Answer 1

answer : If 12n ends with 0 then it must have 5 as a factor.

But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n.

Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique.

So, 5 is not a factor of 12n.

Hence, 12n can never end with the digit 0.