Question

check whether 5n can end with the digit 0 for any natural number n​

Answer 1

Answer:

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 It can be observed that 2 is not in the prime factorisation of 5n. Hence, for any value of n, 5n will not be divisible by 2. Therefore, 5n cannot end with the digit 0 for any natural number n.

Answer 2

Here for any no. to end by digit 0 it should be divisible by 10 or in other words it must contain 2 and 5 in its prime factorization.

5n=(5*1)n

Since, 2 is not in the prime factorization of 5n therefore, 5n cannot end with digit 0 for any natiral no. n.

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