Question

The greatest number, which divides 406 and 1388 to leave 1 and 3 respectively as remainders, is:

• A. 23
• B. 20
• C. 5
• D. 15

Answer 1

Answer:

C. 5

Let the required number be (d).

Given:

• $(406 \div d)$ leaves remainder 1 ⇒ (406 - 1 = 405) is divisible by (d)

• $(1388 \div d)$ leaves remainder 3 ⇒ (1388 - 3 = 1385) is divisible by (d)

So, $(d = \gcd(405, 1385))$

Factorize:

• $(405 = 3^4 \times 5)$

• $(1385 = 5 \times 277)$

Common factor = 5

Answer: 5