What is the greatest common factor of 180 and 225?

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Answer 1 · 2017-02-03T06:13:58

45

Let's do a prime factorization of the two numbers:

$180=2xx90=2xx2xx45=2xx2xx3xx3xx5$
$225=5xx45=color(white)(00000000000000000000)3xx3xx5xx5$

And now let's find what's in the GCF by seeing what is common to both:

2

There are 2s in 180 but not 225, so there are no 2's in the GCF.

3

There are two 3s in both 180 and 225, and so the GCF has two 3s.

5

There is one 5 in 180 and two in 225, and so the GCF has one 5.

And now let's put it all together:

$3xx3xx5=9xx5=45$

$45xx4=180$
$45xx5=225$