# What is the greatest common factor shared by 33 and 60?

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Sep 24, 2016

Greatest Common Factor is $3$

#### Explanation:

Factors of $33$ are $\left\{\textcolor{red}{1 , 3} , 11 , 33\right\}$

Factors of $60$ are $\left\{\textcolor{red}{1} , 2 , \textcolor{red}{3} , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60\right\}$

Common Factors are $\left\{\textcolor{red}{1} , \textcolor{b l u e}{3}\right\}$

and Greatest Common Factor is $3$

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Sep 24, 2016

$3$

#### Explanation:

One method of finding the greatest common factor (GCF) of two numbers goes as follows:

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

• If the remainder is $0$ then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

For our example, we find:

$\frac{60}{33} = 1 \text{ }$ with remainder $27$

$\frac{33}{27} = 1 \text{ }$ with remainder $6$

$\frac{27}{6} = 4 \text{ }$ with remainder $3$

$\frac{6}{3} = 2 \text{ }$ with remainder $0$

So the GCF of $60$ and $33$ is $3$

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