Question

Find the greatest number which divides 2011 and 2623 leaving remainder 9 and case of five each

Answer 1

2011–9 = 2002

2623–5 = 2618.

Factors of

2002 = 2 x7x11x13

2618 = 2x7x11x17

The HCF = 2 x7x11 = 154.

Check: 2011/154 = quotient = 13, and remainder = 9. Correct.

2623/154 = quotient = 17, and remainder = 5. Correct.

The number is 154.