Question

show that any number of form 6^x,x=n can never end with the digit 0​

Answer 1

If 6ⁿ ends with 0 it must have 5 as a factor.

But, 6ⁿ= (2×4)ⁿ = (2ⁿ×3ⁿ). shows that 2 and 3 are the only prime factors of 6ⁿ.

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

So, 5 is not a factor of 6ⁿ.

Hence,6ⁿ. can never end with the digit 0.