Learn and know the methods from which we can able to find H.C.F of any two numbers. For finding the H.C.F of the numbers we have mainly 3 methods. First we will know the names of these three methods.
The 3 methods which are used for finding H.C.F are 1. By writing all the Factors of the numbers 2. Using the Division Method and 3. Using the Prime Factorization. By using any one of these we can find H.C.F of given numbers. By first method i.e. by writing factors, we can find H.C.F only for small numbers. For example, finding H.C.F of 8 and 25 is easy because writing factors of these numbers is a simple thing. But in case, big numbers are given means like 182 and 236 then writing all the factors without missing any factors is a difficult thing. There is a chance of making a mistake here, so you can choose any other method. Now we will learn the process for finding H.C.F of two numbers by all the three methods.
The Process to find the H.C.F of two numbers by writing the factors:
10 and 16 be the two numbers for which we have to find the H.C.F. Follow the below steps for finding the H.C.F of 10 and 16.
Step 1: first write all the factors of the numbers 10 and 16.
Step 2: mark or note down the common factors.
Step 3: find out the in common factors, which is the highest common factor. That’s it. Now you got the H.C.F of 10 and 16.
Follow the above given steps and find the H.C.F of the numbers 10 and 16.
The Factors of the number 10 are 1, 2, 5 and 10
The Factors of the number 16 are 1, 2, 4, 8 and 16
1, 2 are the Common factors of the numbers 10 and 16.
In the common factors (1, 2), the highest common factor is nothing but H.C.F is 2. So, therefore the H.C.F of the two numbers 10 and 16 is equal to 2.
The Process to find H.C.F of two numbers by the Division Method:
Let us take the same numbers which we took in the above process. In the above process we took 10 and 16, so for these numbers we will find H.C.F by Division method.
Step 1: divide small number by bigger number, see the below figure.
Step 2: now make the reminder 6 as the Divisor and Divisor 10 as the Dividend. See the figure for the idea. The same process we need to continue up to remainder becomes zero.
Step 3: in the last step where the remainder becomes zero, in that the Divisor is called as H.C.F. just see the division process given below you can understand. Therefore, the H.C.F of two numbers 10 and 16 is equal to 2.
The Process to find the H.C.F of two numbers by the prime factorization Method:
Follow the steps and find the H.C.F of 10 and 16:
Step 1: both the numbers i.e. 10 and 16, write as a product of the prime numbers
Step 2: then mark or circle common factors.
Step3: multiply the common factors we will get the H.C.F. if there is only one common factor then it is only the H.C.F.
See the below diagram you can understand all the three steps.