How do you find the greatest common factor of the following monomials: 38m, 26m?

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Answer 1 · 2018-03-06T20:53:29

See below

To find the GCF, you must break the constants of the numbers apart to prime numbers.

$38 m =$ $38m=$ $19 \cdot 2 m$ $19*2m$
$26 m = 13 \cdot 2 m$ $26m= 13*2 m$

Now, you must look to see what they have in common. So, the equations both have one $m$ $m$ , so that would go into the GCF.

$m$ $m$

So now you are left with

$19 \cdot 2$ $19*2$
$13 \cdot 2$ $13*2$

Both the equations have two, that also goes into the GCF.

$2 m$ $2m$

You are left with 13 and 19 now. Since those are not common, those would go into your ending equation. Thus, your GCF is $2 m$ $2m$ .