Question

The greatest number, which divides 943 and 1957 to leave 7 and 1 respectively as remainders, is:

• A. 12
• B. 28
• C. 10
• D. 13

Answer 1

Answer:

A. 12

Let the required number be d.

Given:

• 943 leaves remainder 7 ⇒ d divides (943 − 7) = 936

• 1957 leaves remainder 1 ⇒ d divides (1957 − 1) = 1956

So,
$d = \text{HCF of } 936 \text{ and } 1956$
Find HCF

$1956 ÷ 936 = 2 \text{ remainder } 84$
$936 ÷ 84 = 11 \text{ remainder } 12$
84 ÷ 12 = 0

So, HCF = 12