Question

Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.

• A. 153
• B. 154
• C. 151
• D. 150

Answer 1

The correct option is B 154

To find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.

The required number when divides 2011 and 2623 leaves remainders 9 and 5 this means

2011 – 9 = 2002 and 2623 – 5 = 2618 are completely divisible by the number.

Therefore, the required number = H.C.F. of 2002 and 2618

By applying Euclid’s division lemma

2618 = 2002 x 1 + 616

2002 = 616 x 3 + 154

616 = 154 x 4+ 0.

H.C.F. of 2002 and 2618 = 154

Hence, the required number is 154