# What is the greatest common factor of 180 and 225?

45

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

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:

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To find the greatest common factor (GCF) of 180 and 225, you can use prime factorization.

Prime factorization of 180: [ 180 = 2^2 \times 3^2 \times 5 ]

Prime factorization of 225: [ 225 = 3^2 \times 5^2 ]

Now, identify the common prime factors and their lowest powers:

- Both numbers have (3^2) and (5).

Multiply these common prime factors together: [ GCF = 3^2 \times 5 = 9 \times 5 = 45 ]

Therefore, the greatest common factor of 180 and 225 is 45.

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