Question

How do you find the greatest common factor (GCF) of 28 and 42?

Answer 1

Hint: The greatest common factor of a set of the given numbers is the greatest possible value that can divide all the given numbers. To find the GCF, we have to factorize them so that we can get their factors. By multiplying them, we can find out the GCF.

Complete Step by Step Solution:
In this problem, we need to find out the greatest common factor of 28 and 42.
Let us factorize the given numbers to get their factors.
$\Rightarrow 28=2\times 2\times 7$
$\Rightarrow 42=2\times 3\times 7$
If we compare the factors of 28 and 42, we can identify the common factors 2 and 7. We need the greatest common factor. By multiplying the common factors together, we can get the GCF and it will be the greatest value which can divide both 28 and 42.
$\Rightarrow GCF=2\times 7=14$
$\Rightarrow GCF=14$

Hence 14 is the greatest common factor of 28 and 42.

Note:
The least common multiple on the other hand is the least value that can divide all the given set of numbers. To find LCM, we should look for the lowest number among the common factors. For example, the least common factor of 28 and 42 is equal to 2.
We should also note that the GCF of a set of prime numbers is equal to 1. Sometimes, if the prime numbers are equal, the GCF is the prime number itself ie., GCF of 7 and 7 is equal to 7.