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How do you find the GCF of 16, 56?

1 Answer

Jan 7, 2017

The GCF is $8$ $8$

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: $16, 56$ $16, 56$

Subtract $16$ $16$ from $56$ $56$ to get: $16, 40$ $16, 40$
Subtract $16$ $16$ from $40$ $40$ to get: $16, 24$ $16, 24$
Subtract $16$ $16$ from $24$ $24$ to get: $16, 8$ $16, 8$
Subtract $8$ $8$ from $16$ $16$ to get: $8, 8$ $8, 8$

So the GCF is $8$ $8$

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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 $0$ $0$ then the smaller number is the GCF.
Otherwise repeat with the smaller number and the remainder.

So in our example:

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

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

So the GCF is $8$ $8$

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