NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 4

Question.  4

If the HCF of 65 and 117 is expressible in the form \(65m – 117\), then the value of \(m\) is

(A)

4

(B)

2

(C)

1

(D)

3

Handwritten Notes

If the HCF of 65 and 117 is expressible in the form \(65m – 117\), then the value of \(m\) is 1
If the HCF of 65 and 117 is expressible in the form \(65m – 117\), then the value of \(m\) is 2
If the HCF of 65 and 117 is expressible in the form \(65m – 117\), then the value of \(m\) is 3

Video Explanation:

Detailed Answer with Explanation:

We first find HCF(65, 117) using Euclid’s division algorithm:

\(117 = 65 \times 1 + 52\)

\(65 = 52 \times 1 + 13\)

\(52 = 13 \times 4 + 0\)

So the HCF is 13.

Now, it is given that HCF can be expressed as \(65m - 117\).

So, \(65m - 117 = 13 \Rightarrow 65m = 130 \Rightarrow m = 2\).

Thus, the required value of \(m\) is 2.

Open NCERT PDFOpen NCERT Answers PDF
NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 1: Real Numbers – Exercise 1.1 - Multiple Choice Questions | Detailed Answers