Question

What is the greatest common factor of \[8\],\[12\] and \[24\] ? Provide an explanation of how to find great common factors .

Answer 1

Hint:In this question , we need to find out the greatest common factor of the given three numbers. The greatest common factor (GCF) is nothing but the greatest factor that is common to two or more numbers. In order to find the greatest common factor of the given numbers, the method of prime factorisation is used . First we need to list out the prime factors of the given three numbers. After listing the factors of the given numbers, we need to find any of the common factors for each number. Using this we can find out the greatest common factor of \[8\],\[12\] and \[24\] .

Complete step by step solution:
Given, \[8\],\[12\] and \[24\]
Here we need to find out the greatest common factor of \[8\],\[12\] and \[24\]
First, we can write the factors of the given number.
Factors of \[8\]
\[\Rightarrow 2 \times 2 \times 2\]
Factors of \[12\] ,
\[\Rightarrow 2 \times 2 \times 3\]
Factors of \[24\] ,
\[\Rightarrow 2 \times 2 \times 2 \times 3\]
On seeing the factors of the given numbers, the greatest common factor of these three numbers is \[2 \times 2\]
On multiplying,
We get the greatest common factor of these three numbers is \[4\]
Hence the greatest common factor of \[8\],\[12\] and \[24\] is \[4\] .
The greatest common factor of \[8\],\[12\] and \[24\] is \[4\] .

Note:
We may get confused with GCF and LCM. GCF is the greatest common factor among the given numbers whereas LCM is the smallest number (excluding zero) that is a multiple of both of the numbers. The greatest common divisor is useful in reducing the fractions to the lowest terms. The greatest common divisor can also be utilized in finding the least common multiple of two numbers when the greatest common factor is known. The relationship is given by,
\[\text{lcm}\left( a,\ b \right) = \dfrac{\left| \text{a.b} \right|}{\text{gcf}\left( a,\ b \right)}\]