Check whether 6n can end with the digit 0 for any natural number n.

Given

A number 6n

Find out

We need to check whether it can end with zero

Solution

We know that any number is multiplied by 5 or 10 or by the multiples of 10 ends with zero.

If the number 6n ends with the digit zero (0), then it should be divisible by 5.

We know any number with the unit place as 0 or 5 is divisible by 5.

Prime factorization of 6n can be expressed as = (2×3)n

Therefore, the prime factorization of 6n doesn’t contain prime number 5.

Hence, it is obvious that for any natural number n, 6nis not divisible by 5

Thus it proves that 6n cannot end with the digit 0 for any natural number n.

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