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Question

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

A
153
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B
154
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C
151
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D
150
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Solution

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


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