What is the GCF of 210 and 252?

Question

Jeremiah Andrews · Accepted Answer

#42#

The following is one method for determining the GCF of two numbers:

#color(white)()# Divide the larger number by the smaller to give a quotient and remainder.

The GCF is the smaller number if the remainder is zero.

If not, repeat with the remainder and the smaller number.

#color(white)()# In our example:

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

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

So the GCF is #42#

Julian Avila · Answer

#GCF = 42#

If we only know the multiplication tables up to 12 x 12, we should be able to find the GCF fairly quickly in most situations.

Occasionally a larger number that is unknown to us may be included; this is one instance of that.

You can write all of the prime factors by mentally using factor trees.

(for example: #210 = 10xx21 = 2xx5xx3xx7#)

It is beneficial to have a backup plan in place in the event that visual inspection fails to locate the GCF.

Write each number as the product of its prime factors to find the GCF (and the LCM).

#color(white)(xxxx) 210 = 2color(white)(xxx)xx3xxcolor(white)(x)xx5xx7# #color(white)(xxxx) 252 = 2xx2xx3xx3color(white)(xxx)xx7#

#GCF =color(white)(xxx)2color(white)(xxx)xx3color(white)(xxxx.x)xx7 =42#

This makes it abundantly evident that 42 is the common factor.

This format makes it simple to calculate the LCM if we need it: Add all the factors in each column, making sure not to count the same factors twice.

Everly Taylor · Answer

undefined The Greatest Common Factor (GCF) of 210 and 252 is 42.