Question

Find the HCF by successive division method: 156, 182.

Answer 1

Hint: Begin by selecting the greater of the numbers 156 and 182 as the dividend and the smaller one as the divisor. The non-zero remainder thus obtained will be the divisor in the next step and the divisor of the previous step will be the dividend. Repeat this until you get zero as the remainder.
The last divisor of this method is the correct answer.

Complete step by step solution:
We are given two numbers 156 and 182.
We are asked to find the HCF of these two numbers.
The method to be used is the successive division method.
The steps for successive division method are as follows:
1) Choose the greater of the two numbers to be the dividend and the other one will be the divisor.
Upon division, you may get a non-zero remainder. If the remainder is zero, then this divisor is the required HCF. If not, then move on to the next step.
2) Consider the non-zero remainder obtained in step 1 as the next divisor and the divisor of step 1 as the next dividend. Find the remainder.
If the remainder is zero, then the process steps and the divisor of this step is the required HCF.
If the remainder is non-zero, then we repeat step 2 until we get the remainder as zero.
3) The last divisor of this method would be the HCF of the given numbers.
Now, let’s apply these steps to the numbers 156 and 182.
We know that 182 is greater than 156.
Therefore, our dividend will be 182 and divisor will be 156.
We will use the following way to show this successive division

As we can see that, the remainder for the divisor 156 is 26.
So, we treat 26 as the next divisor and 156 as the dividend.
Now, the remainder becomes zero.
Therefore, we get the last divisor as 26.
Hence the highest common factor (HCF) of 156 and 182 is 26.

Note: Some students forget to change the dividend at each step. Retaining this from the previous will lead you to an incorrect answer.