Question

How do you find the greatest common factor of 8, 20 and 44?

Answer 1

Hint: The greatest common factor of the given numbers, 8, 20 and 44 can be found out by first finding their prime factors. So, try to express each term in terms of its prime factors. Then, take all the common factors among them. The greatest common factor will be our required answer.

Complete step-by-step answer:
Prime factors: The prime factors of any number can be defined as the prime numbers that are multiplied together to give the number itself.
We have to find the prime factors of each number separately.
As we know, the prime factors of ‘8’ are
$8=2\times 2\times 2$
The prime factors of ‘20’ are
$20=2\times 2\times 5$
The prime factors of ‘44’ are
$44=2\times 2\times 11$
Greatest common factor: It can simply be defined as the largest of the common factors.
From the above we can conclude that the common factors among these three numbers are $2\times 2$
So the greatest common factor is $2\times 2=4$.
This is the required solution.

Note: It should be remembered that each and every term should be expressed in terms of prime factors only. For example we cannot write the factors of ‘8’ as $8=4\times 2$. The same is applicable for the rest. The greatest common factor can be used in the simplification of a fraction. For example if we have to simplify $\dfrac{12}{30}$. First we can find the common factors of ‘12’ and ‘30’ are 1,2,3 and 6. So the greatest common factor is 6. Then by dividing the numerator and denominator by the greatest common factor we can get the simplified form of the fraction as
$\dfrac{12}{30}=\dfrac{12\div 6}{30\div 6}=\dfrac{2}{5}$