Question

The greatest number, which divides 1477 and 671 to leave 0 and 6 respectively as remainders, is:

• A. 17
• B. 16
• C. 20
• D. 7

Answer 1

Answer:

D. 7

Let the required number be d.

Given:

• 1477 leaves remainder 0 ⇒ d divides 1477

• 671 leaves remainder 6 ⇒ d divides (671 − 6) = 665

So, d = HCF of 1477 and 665

Find HCF

$1477 - 665 = 812$
$812 - 665 = 147$
$665 ÷ 147 = 4 \text{ remainder } 77$
$147 ÷ 77 = 1 \text{ remainder } 70$
$77 ÷ 70 = 1 \text{ remainder } 7$

70 ÷ 7 = 0

So, HCF = 7