Question

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

Answer 1

Answer:

Find the greatest number which

divides 2011 and 2623,

leaving remainders 9 and 5

respectively. *

Answer 2

Answer:

To find the greatest number which when divides 2011 & 2623 leaving the remainders 9 & 5 respectively.First,we subtract the remainder from the given numbers & then calculate the H.C.F of new numbers.

Given numbers are 2011 & 2623 & remainders are 9 & 5.

Then,new numbers after subtracting remainders are:

2011 - 9 = 2002 & 2623 - 5 = 2618

Now,we  have to find the H.C.F of 2002 & 2618

By applying Euclid's division lemma,a = bq+r

Let a = 2618 & b = 2002

2618 = 2002 x 1 + 616

2002 = 616 x 3 + 154

616 = 154 x 4 + 0

Here remainder is zero,& the last divisor is 154.

So,H.C.F of 2002 & 2618 is 154.

Hence,the required greatest number is 154.

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