Question

What is the greatest number which when divides 92 and 215, leaves remainders 7 and 11, respectively?

• A. 17
• B. 23
• C. 21
• D. 19

Answer 1

Answer:

A. 17

Let the required number be (d).

Given:

• $(92 \div d)$leaves remainder 7 ⇒ $(92 - 7 = 85)$is divisible by (d)

• $(215 \div d)$ leaves remainder 11 ⇒ $(215 - 11 = 204)$ is divisible by (d)

So, (d) is the HCF of 85 and 204.

• $85 = 5 \times 17,\quad 204 = 2^2 \times 3 \times 17$
  

Common factor = 17

Answer: 17