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# Find the H.C.F of the following numbers using prime factorization method. 540, 980.

Last updated date: 20th Sep 2024
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Hint: First, we should know the concept of prime factorization i.e. finding which prime numbers multiply together to make the original number. Also, the concept of highest common factor (HCF) i.e. the greatest number which can divide the given numbers. So, here we will first find out prime factors of 540, 980 and then we find which factors are common in both that will be our answer.

We know the definition of highest common factor (HCF) given as the greatest number which can divide the given numbers. Also, Prime factorization is finding which prime numbers multiply together to make the original number. To understand this, we will take an example: Suppose we have to find factors of number 12. So, first we will see whether the number is divisible by 2 or not. So, we will get $12=2\times 6$. Now, we will take 6 and see whether it is divided by 2 or not. So, we will get $12=2\times 2\times 3$. Now, we know that 3 is a prime number so no need to further solve this. Hence, we get our prime factors 2 and 3.
\begin{align} & 2\left| \!{\underline {\, 540 \,}} \right. \\ & 3\left| \!{\underline {\, 270 \,}} \right. \\ & 3\left| \!{\underline {\, 90 \,}} \right. \\ & 3\left| \!{\underline {\, 30 \,}} \right. \\ & 2\left| \!{\underline {\, 10 \,}} \right. \\ & 5\left| \!{\underline {\, 5 \,}} \right. \\ \end{align}
Factors of 540 are $540=2\times 3\times 3\times 3\times 2\times 5$
\begin{align} & 2\left| \!{\underline {\, 980 \,}} \right. \\ & 2\left| \!{\underline {\, 490 \,}} \right. \\ & 5\left| \!{\underline {\, 245 \,}} \right. \\ & 7\left| \!{\underline {\, 49 \,}} \right. \\ & 7\left| \!{\underline {\, 7 \,}} \right. \\ & 5\left| \!{\underline {\, 5 \,}} \right. \\ \end{align}
Factors of 980 are $980=2\times 2\times 5\times 7\times 7$
Now, if we compare both the factors, we can see that the highest common factor in both is $2\times 2\times 5=20$ .