SOLUTION: 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 Ma

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.

RELATED QUESTIONS
why is it when a odd number is added to an odd number its always even, and when a odd... (answered by RAY100)

If a is an odd number, b an even number, and c an odd number, which expression will... (answered by Edwin McCravy,ikleyn)

write an expression for the sum of 1 and twice a number n. If you let n be any odd... (answered by Fombitz)

suppose I added up a long list say thousands of natural numbers with the property that... (answered by Edwin McCravy)

Suppose you are tossing a die, what is the probability that you will get an odd... (answered by richwmiller)

the sum of a whole number and a odd number always results in a odd number (answered by Edwin McCravy,josgarithmetic)

Can you add 3 odd number and get... (answered by Alan3354)

Factor of 75. Two-digit number Sum of digits, odd What is________? Thank you for... (answered by richard1234)

when y is an odd number in an algebraic equation why does the always equal an even number (answered by Alan3354)