Question

What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

Options

• 15

• 16

• 9

• 5

Answer 1

16

Explanation:

If a number leaves remainder 5 when dividing 245 and 1029, it divides 245 – 5 = 240 and 1029 – 5 = 1024 exactly.

So, the required number is HCF(240, 1024).

Since, 240 = 2⁴ × 3 × 5 and 1024 = 2¹⁰, their HCF = 2⁴ = 16.