Question

Check whether 12^n end with the digit 0, where n is any natural number

Answer 1

Step-by-step explanation:

If the number, 12^n, for any n, were to end with the digit zero, then it would be divisible by 5. That is, the prime factorisation of 12^n would contain the prime number 5. This isn't possible because 12^n = (2×2×3)^n ; In the factorisation of 12^n here the factor is only 2 and 3 not 5, and it is necessary for every number which ends with zero having its one factor 5, and Here the factor isn't 5. So, 12^n doesn't end with the digit 0, where n is any natural number.