If $M$ is an even number.

Then what are the possible even factors of $M$ ?

I am thinking that maximum possible even factors are $\frac M2,\frac M4,\frac M8, \frac M{16}$ and so on Are there any even factors other than that ?

Am I correct ?

Please help me. Thanks in a advance.

  • $\begingroup$ A number is called "even" if 2 is a factor. A number is called "odd" if 2 is not a factor. 70 is even because 2 is a factor but the other factors are 5 and 7. And you can't get 5 or 7 from 70/2, 70/4, 70/8, etc. Knowing a number is even gives you no other information other than 2 is a factor. $\endgroup$ – Apprentice Queue Nov 20 '13 at 22:15

If $M=30$, then $M/2=15$ is not an even factor of $M$; however $2$, $6$, $10$, and $30$ are.

In fact, if $M=2^ns$, where $s$ is odd, then the even factors of $M$ are $2^mt$, where $1\le m\le n$ and $t$ is any factor of $s$.


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