# How do you find the GCF of 16, 56?

Jan 7, 2017

The GCF is $8$

#### Explanation:

Method 1 - Subtraction

One method of finding the GCF of two positive numbers goes as follows:

• If the two numbers are equal to the same value then that is the GCF.

• Otherwise subtract the smaller number from the larger and repeat.

So in our example:

Given: $16 , 56$

• Subtract $16$ from $56$ to get: $16 , 40$

• Subtract $16$ from $40$ to get: $16 , 24$

• Subtract $16$ from $24$ to get: $16 , 8$

• Subtract $8$ from $16$ to get: $8 , 8$

So the GCF is $8$

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Method 2 - Division

Given two numbers, you can find their GCF 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.

So in our example:

$\frac{56}{16} = 3 \text{ }$ with remainder $8$

$\frac{16}{8} = 2 \text{ }$ with remainder $0$

So the GCF is $8$