Question

Prove that there us no natural number for which (6)^n ends with the digit zero.

Answer 1

Here is your solution

If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5

Prime factorisation of 6n = (2 ×3)n

It can be observed that 5 is not in the prime factorisation of 6n.

Hence, for any value of n, 6n will not be divisible by 5.

Therefore, 6n cannot end with the digit 0 for any natural number n.

Answer 2

heya!!

hope my answer helps you ⤵️⤵️

If any digit has 10 . it mean it is divisible by 2 and 5.

we can get 2×5 = 10.

but we won't get it for for 6n

6n is not divisible by 2.

so it cannot end with an zero.

hope my answer helps you ✌