Is it true that every positive integer different from 1 can be expressed as a product of non-negative power of 2 and an odd number. What is the odd number when there are no prime factors.
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Let the number of times the positive integer k can be successively divide by 2 be n. Then, k=2n×(productofk′sprimefactorsotherthan2) Note that this includes n=0 for odd numbers. The prime factors other than 2 must be odd, so their product is odd. When there are no prime factors other than 2 we can can still multiply 1, which is odd.
Thus the correct answer is 1 as that is the odd number when there are no prime factors.