Question

If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is
1. 4
2. 2
3. 1
4. 3

Answer 1

Correct Answer - Option 2 : 2

Concept: 

Euclid's division lemma: Given positive integers a and b there exist whole numbers q and r satisfying,

a = bq + r, where, 0 ≤ r ≤ b

Calculation:

Using Euclid's division lemma, 

117 = 65 × 1 + 52

⇒ 65 = 52 × 1 + 13

⇒ 52 = 13 × 4 + 0

∴ HCF(65, 117) = 13

According to question,

65m - 117 = 13

⇒ 65m = 117 + 13 = 130

⇒ m = 2