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

Solution:

Using Euclid’s division algorithm,

b = aq + r, 0 ≤ r < a

We know that

dividend = divisor x quotient + remainder

117 = 65 × 1 + 52

65 = 52 × 1 + 13

52 = 13 × 4 + 0

HCF (65, 117) = 13 --- (1)

Also, given that,

HCF (65, 117) = 65m - 117 --- (2)

By equating (1) and (2),

65m - 117 = 13

65m = 130

m = 2.

Therefore, the value of m = 2

✦ Try This: What is the HCF of 225 and 867

867 is greater than 225

Applying Euclid’s division algorithm,

867 = 225 × 3 + 192

225 = 192 × 1 + 33

192 = 33 × 5 + 27

33 = 27 × 1 + 6

27 = 6 × 4 + 3

6 = 3 × 2 + 0

Therefore, HCF(867, 225) = 3

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

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NCERT Exemplar Class 10 Maths Exercise 1.1 Problem 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

Summary:

If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is 2. Hence Option B is the correct answer.

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