# How do you find the greatest common factor of 80, 16?

Nov 1, 2016

#### Answer:

The Greatest Common Factor of 80, 16 is 16

#### Explanation:

Method suggested :

• Find the prime factors of each number :

$80 = 2 \times 4 \times 10 = 2 \times 2 \times 2 \times 2 \times 5 = {2}^{4} \times 5$
$16 = 4 \times 4 = 2 \times 2 \times 2 \times 2 = {2}^{4}$

• Find the common prime factors : in this case there's only 2
• If you have many, take the smaller of the exponents of theses common prime factors and multiply them together to find the GCF, for this example $G C F = {2}^{4} = 16$

Example : Find the GCF of 90, 24

$90 = 9 \times 2 \times 5 = {3}^{2} \times {2}^{1} \times 5$
$24 = 3 \times 4 = {3}^{1} \times {2}^{2}$

• The common factor primes are 2 and 3
• The smaller exponents of each are ${2}^{1} \mathmr{and} {3}^{1}$
• Multiply those and the $G C F = {3}^{1} \times {2}^{1} = 6$

I hope that was clear, you can find more in the link below :