Question 41508
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If you have an odd number it has the form 2a+1
Assume that 2a+1 has an even factor, 2b and another
factor which may or may not be even.
If the 2nd factor is even, 2c then 2b(2c)=2a+1
Then 2(b2c)=2a+1
But 2(b2c) is even so cannot equal 2a+1.
If the 2nd factor is odd, 2c+1, then 2b(2c+1)=2a+1
Then 2[b(2c+1)]=2a+1
But 2[b(2c+1)] is even and cannot equal 2a+1.
Therefore the factors of every odd number are odd.
Cheers,
Stan H.