Question

show that 12^n cannot end with 0 or 5

Answer 1

IF 12^N END WITH 0 OR 5 THEN IT'S PRIME  FACTORIZATION CONTAIN  5
HENCE,
12=3×4
IT DOES NOT CONTAIN 5 SO , IT MEANS 12^N DOES NOT END WITH 0 OR 5.
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Answer 2

for the number 12^n  to end with digit zero for any natural number n, it should be divisible by 5. this means that the prime factorization of 12^n should contain the prime number 5. but it is not possible because 12^n=2^2n* 3^n. so, 2 and 3 are the primes in the factorization of 12^n.since 5 is not present in the prime factorization, there is no natural number n for which 12^n ends with the digit zero.