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| 1. |
Show that 12th cannot end with digit 0 or 5 for any natural number \'n\' |
| Answer» If 12n ends with 0 then it must have 5 as a factor.But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n.Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique.So, 5 is not a factor of 12n.Hence, 12n can never end with the digit 0. | |