# What is the greatest common factor of 42, 126, and 210

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Given the numbers 42, 126, and 210

We need to find the greatest common factor ( GCF)

First we will factor each numbers.

==> 42 = 2*3*7

==> 126 = 2*3*3*7

==> 210 = 2*3*5*7

Now we will determine the common factors between all three numbers and multiply.

We notice that the common factors are 2 , 3 and 7.

**Then the greatest common factor = 2*3*7 = 42**

To find the greatest common factor of 42, 126, and 210, we find the prime factors of the 3 numbers.

42 = 7 * 3 * 2

126 = 2 * 7 * 3 * 3

and 210 = 5 * 2 * 7 * 3

Now taking the common terms we have 7 , 3 and 2

7*3*2 = 42.

**Therefore the greatest common factor or GCF is 42**