Question

check whether 12n ends with zero for any natural number.​

Answer 1

Answer:

12n Can't end with the digit zero (0) because for ending with digit zero (0) it is necessary for having the factor 2 and 5 but here the factor is 2 × 2 × 3. so, 12n can't end with the digit zero (0) .

Answer 2

Answer:

If the number 12^n, where n is a natural number, were end with the digit 0 , then it would be divisible by 2 and 5 both

12^n = (2×2×3)^n

There are only prime factor of 12 is 2 and 3.

5 is not prime factor of 12.

By Fundamental theorem of Arithmetic Uniqueness Property guarantee that there are no other prime number in the factorisation of 12^n.

So, THERE IS NO NATURAL NUMBER OF N TO WHICH 12^n ENDS WITH DIGIT ZERO

HOPE IT HELPS YOU.