What are the greatest common factor of 42 and 126?

Answer 1

The greatest common factor of 42 and 126 is 42. For future reference, to find greatest common factors, list all of the factors of each number, find all factors in common that the numbers have, and choose the largest one. For example,

The factors of 42 are:

1, 2, 3, 6, 7, 14, 21, and 42

The factors of 126 are:

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.

The common factors between 42 and 126 are:

1, 2, 3, 6, 7, 14, 21, and 42.

The largest number in the grouping of common factors is 42, therefore the greatest common factor between 42 and 126 is 42.

Of course that's the long and tedious way.

Trick: Trial and error

1) Try if you can evenly divide the smaller number by the larger one. That is find a number a such that a x 42 = 126. You can easily find a this case, a = 2. So, the smallest common factor is 42.

2) If you cannot find one right away, divide them by the obvious common factor, in this case, since they are both even, divide by 2. Then try 1) again. But do this only if 1) fails

repeat 2) for a while.

If you cannot find one for, say a long time, use the long way or

You keep trying and reduced it to two numbers that obviously have no common factor, then you multiply all the factors you had from 2)'s and that's your answer (so something like 2 x 2 x 2 x ......x 2 x 3 x 3 x ..... = 42)