Question

find the greatest number which divides 2011 and, leaving remainder 9 and 5 respectively.
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Answer 1

Answer= Subtract 9 from 2011 and 5 from 2423 to get 2002 and 2418, respectively, and find their HCF to get the answer.

2011–9 = 2002

2423–5 = 2418

2002 = 2x7x11x13

2418 = 2x3x13x31

HCF = 2x13 = 26.

Check 2011/26 = 77 as quotient and 9 as remainder. Correct.

2423/26 = 93 as quotient and 5 as remainder. Correct.

So the greatest number is 26.