# What is the GCF of 210 and 252?

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In most cases we should be able to find the GCF fairly easily by just knowing the multiplication tables up to 12 x 12.

Sometimes a bigger number might be included which we do not know well. This is just such a case.

Using factor trees mentally will allow you write all the prime factors.

(for example:

It is good to have a method available for cases when we cannot find the GCF by inspection.

In order to find the **GCF** (and the LCM) write each number as the **product of its prime factors** .

From this it is very clear that the common factor is 42

If we needed the LCM it can be calculated easily from this format:

Include each column of factors, do not count factors that are in the same column twice.

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One way of finding the GCF of two numbers is as follows:

Divide the larger number by the smaller to give a quotient and remainder.

If the remainder is zero then the smaller number is the GCF.

Otherwise, repeat with the smaller number and the remainder.

In our example:

#252 / 210 = 1# with remainder#42#

#210 / 42 = 5# with remainder#0#

So the GCF is

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