Question

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

Answer 1

Hint: The factor that divides a given number of terms is the greatest common factor. Write this in the form of the prime numbers in variables in order to find the largest common factor of these three monomials, and then find the factor that is common in all terms.

Formula used:
In order to find the prime factors, we start by dividing the number by the least prime number $2$ and divide until we get a remainder. After that, we divide it by $3,\;5,\;7,$ and so on until we are left with prime numbers only .Secondly, we write all the prime numbers in the multiplication form. For example for $12$, we start by dividing $12$ with $2$, and after dividing twice, we get $3$ as remainder which is also a prime number so we write it as $2 \times 2 \times 3$. And the product of prime numbers that are common, form the Greatest Common Factor.

Complete step by step solution:
Firstly, in order to find the greatest common factor of $80,\,16$ we write the prime factors of the all the terms:
For the first term, i.e. $80$
$80 = 2 \times 2 \times 2 \times 2 \times 5$
For the second term, i.e. $16$
$16 = 2 \times 2 \times 2 \times 2$
For the two terms, the greatest factors that are common are
$
   = 2 \times 2 \times 2 \times 2 \\
   = 16 \\
 $
Therefore, the greatest common factor of the terms $80,\,16$ is $16$

Note: In this question, always start with the lowest prime factor only. Starting with a factor other than the lowest one may be troublesome, because when you start with low to high prime numbers then you can calculate the greatest common factor easily.