Another Problem About Parity
Number Theory
Level
1
If you divide an odd number by an even number, how often do you end up with an integer?
Always
Sometimes
Never
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1 solution
Let's say this problem is represented by a/b=c, where a is odd and b is even. We can change this problem to multiplication by switching the positions of the dividend and quotient, getting c b=a. Remember that an integer multiplied by an even number is always even, because multiplication is essentially repeated addition, where you add the even number b an integer amount of times. An even number added to an even number is still even. That means that if c was an integer, then c b needs to be even, but since a is odd, c can't be an integer.