Question

The H.C.F. of 65 and 117 using Euclid's division lemma is .

• A. 11
• B. 12
• C. 13

Answer 1

The correct option is C 13

Step 1: Since $117>65,$ we apply Euclid's division lemma to 117 to get
$117=65\times 1+52.$
Step 2: Since $52\ne 0,$ we apply the division lemma to 65 and 52 to get
$65=52\times 1+13.$
Step 3: Since $13\ne 0,$ we apply the division lemma to 52 and 13 to get
$52=13\times 4+0.$
Since the divisor at this step is 13 and remainder is zero, the HCF of 117 and 65 is 13.