# How can i prove that a multiple of 4 is a multiple of 12?

1. Mar 29, 2005

How can i prove that a multiple of 4 is a multiple of 12?

2. Mar 29, 2005

### xanthym

You can't ... because it's NOT true.
Example:
(2)*(4)=(8) is NOT a {Multiple of (12)}

However, you can prove that a {Multiple of (12)} is a {Multiple of (4)}. Begin by factoring (12):
(12) = (4)*(3)
Now consider the integer "k" multiple of (12) given by (12)*k, where {k = 1, 2, 3, ...}:
{"k" Multiple of (12)} = (12)*k = {(4)*(3)}*k = (4)*{(3)*k} = (4)*m
where "m" is a positive integer. Thus:
{Multiple of (12)} IS A {Multiple of (4)}

~~

Last edited: Mar 29, 2005
3. Mar 29, 2005

### HallsofIvy

Staff Emeritus
It is true that a multiple of 12 is a multiple of 4- just the opposite of the original post. That's true because "multiple of 12" MEANS "12 times some integer". If x is a multiple of 12, then x= 12n for some integer n. "Multiple of 4" MEANS "4 times some integer". Of course, if x is a multiple of 12 then x= 12n= 4(3n) so that x is 4 times the integer 3n: a multiple of 4.