Find the greatest number which divides 2011 and 2623 leaving remainder

1.	Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.
Answer» For the question it’s understood that, 2011 – 9 = 2002 and 2623 – 5 = 2618 has to be exactly divisible by the number. Thus, the required number should be the H.C.F. of 2002 and 2618 Applying Euclid’s division lemma, we get 2618 = 2002 x 1 + 616 2002 = 616 x 3 + 154 616 = 154 x 4 + 0. (Here the remainder becomes 0) And hence the H.C.F. (2002, 2618) = 154 ∴ The required number is 154.

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

Answer»

For the question it’s understood that,

2011 – 9 = 2002 and 2623 – 5 = 2618 has to be exactly divisible by the number.

Thus, the required number should be the H.C.F. of 2002 and 2618

Applying Euclid’s division lemma, we get

2618 = 2002 x 1 + 616

2002 = 616 x 3 + 154

616 = 154 x 4 + 0. (Here the remainder becomes 0)

And hence the H.C.F. (2002, 2618) = 154

∴ The required number is 154.