Question

Show that 12power n cannot end with the digit 0 or 5 for any natural number N? ??

Answer 1

Answer:

Here, Number=12n where n stand for any natural number . Now , For 12n to end with 0, it should have 2 as well as 5 in its Prime factors to end with 0, Also to end with 5 , it requires at least a single multiple of 5 in its Prime Factors, So 12n cannot end with the digit 0 or 5.

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Answer 2

Answer:

prime factarization of 12 = 2×2×3

any no. which has a factor 2^m × 5^n end with zero

but 12 has no such factor

According to fundamental theorem of arithmetic

every no. has unique factarization.

hence 12 cannot end with zero or 5