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How do you find the GCF of $12,24$ and $36?$

seo-qna
Last updated date: 14th Jul 2024
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Answer
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Hint: We know that the GCF is the Greatest Common Factor of the numbers. We will find the factors of the given numbers. Among them, we will find the greatest factor that is common to all the numbers.

Complete step-by-step answer:
Let us consider the given numbers $12,24$ and $36.$
We are asked to find the Greatest Common Factor of the given numbers.
We know that, as the name suggests, we need to find the factor that is both the greatest and the common one among the factors of the given numbers.
Let us first list down the factors of the given numbers.
We will first write the factors of the number $12$ down. They are, $1,2,3,4,6,$ and $12.$
Now, we will write down the factors of the number $24.$ They are, $1,2,3,4,6,8,12$ and $24.$
Finally, we will write the factors of the number $36.$ They are, $1,2,3,4,6,9,12,18$ and $36.$
Now, we need to write the factors that are common in the lists of the factors of the given number.
We will get $1,2,3,4,6$ and $12.$
We need to choose the highest one among the common factors and that will be the Greatest Common Factor of the given numbers.
We can see, $12$ is the greatest.
Hence the GCF of the given numbers is $12.$

Note: We know that the GCF stands for the Greatest Common Factor. It can also be called Highest Common Factor or Greatest Common Divisor. Similarly, we have LCM which stands for the Least Common Multiple. As the name says, it is the smallest multiple of the numbers concerned.