Question 41508This question is from textbook
: During a lesson on factoring natural number, Marcia said, "I think when you factor an odd number, you always get odd factor."
a, Is Marcia correct?
b, How could you convince Marcia and the rest of the class that Marcia is or is not correct.
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ----------------------------------------------
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.
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