Question

prove that 6n never end with zero​

Answer 1

HEY MATE !!!

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.

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Answer 2

6^n = (3x2)^n

we can write the prime factorisation in

only on way

To get zero we should have 2 and 5 in

prime factoristion

so 6^n cannot end with zero because

there is no 5 in it