Answer

Verified

348.5k+ views

**Hint**: First we recall Euclid's algorithm; we can calculate the HCF of two integers by using Euclid’s division algorithm. First assume the greater number as $ a $ and smaller number as $ b $ . Now, express the numbers in the form of $ a=bq+r $ where, $ q\And r $ are unique integers. We follow the same procedure until we get remainder zero.

**:**

__Complete step-by-step answer__We have given that numbers $ 1651 $ and $ 2032 $ .

We have to find the HCF by using Euclid’s algorithm.

Now, we compare both numbers, we get

$ 2032>1651 $

Let us assume $ 1651=b $ and $ 2032=a $ .

Now, expressing the numbers in the form $ a=bq+r $ , we get

$ 2032=\left( 1651\times 1 \right)+381 $

As $ 381\ne 0 $, we repeat the same process with $ 1651 $ and $ 381 $.

Now, assume $ 1651=a $ and $ 381=b $.

Now, expressing the numbers in the form $ a=bq+r $ , we get

$ 1651=\left( 381\times 4 \right)+127 $

As $ 127\ne 0 $ , we repeat the same process with $ 381 $ and $ 127 $ .

Now, assume $ 381=a $ and $ 127=b $ .

Now, expressing the numbers in the form $ a=bq+r $ , we get

$ 381=\left( 127\times 3 \right)+0 $

Since the remainder is zero, we can not proceed further.

The HCF of $ 1651 $ and $ 2032 $ is $ 127 $.

**Note**: The basis of Euclid’s algorithm is Euclid’s division Lemma. The word Lemma is already a proven statement used to prove other statements. On the other hand, an algorithm is a set of steps used to solve a problem. Euclid’s division lemma is used to prove other theorems. Euclid’s division algorithm is follows the form:

$ \text{Dividend=}\left( \text{Divisor}\times \text{Quotient} \right)+r\text{emainder} $

Recently Updated Pages

What are the Advantages and Disadvantages of Algorithm

How do you write 0125 in scientific notation class 0 maths CBSE

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

You are awaiting your class 10th results Meanwhile class 7 english CBSE

Which one of the following was not the cause of the class 10 social science CBSE

Which one of the following cities is not located on class 10 social science CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE