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ua Example 5 : Consider the numbers 4", where n is a natural number. Check whetherai there is any value of n for which 4" ends with the digit zero. |
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Answer» :If the number 4n, for any n, where to end with digit zero, then it would be divisible by 5. That is the prime factorization of 4n would contain the prime 5. This is not possible because 4n = (2)²n ; so the only prime factorization of 4n is 2. So the uniqueness of the fundamental thm of arithmetic guarantees that there are no other prime in the factorization of 4n. So there is no natural number n for which 4n ends with digit zero. |
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