Question

Prove that 'n' is a natural number then 12 th no end with 0 and 5 ?

Answer 1

Answers:

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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.