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| 1. |
Show that numbers 8n can never end with digit 0 for any natural number n. |
| Answer» If any numbr ends with 0, then it must be divisible by 10 .Hence it should have 5 and 2 as a factors. Now the factorization of 8n\xa0are:{tex}\\therefore 8 ^ { n } = ( 2 \\times 2 \\times 2 ) ^ { n } = 2 ^ { n } \\times 2 ^ { n } \\times 2 ^ { n }{/tex}Hence 5 is not in the factors of 8n.From the fundamental theorem of arithmetic, we know that the prime factorization of every composite number is unique.So it is clear that 8n is not divisible by 10.{tex}\\therefore{/tex}\xa08n\xa0can never end\xa0with 0. | |