Question

greatest number that divides 2011 and 2623 leaving 9 and 5 remainder respectively

Answer 1

Answer:

The Answer Is 154

Step-by-step explanation:

First ,we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

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

Then ,new numbers after subtracting remainders are :

2011 – 9 = 2002 and 2623 – 5 = 2618

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

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

Let a = 2618 and b = 2002

2618 = 2002 x 1 + 616

2002 = 616 x 3 + 154

616 = 154 x 4+ 0.

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

So H.C.F of 2002 and 2618 is 154

Hence, the required greatest number is 154.

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Answer 2

Answer:154

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Step-by-step explanation:FIRSTLY TO FIND THE NO. IN CASE I AS WE KNOW THAT THE REMAINDER HA STO BE 9

SO SUBTRACT 9 FROM 2011

2011-9=2002

SIMILARLY IN CASE 2 THE REMAINDER HAS TO BE 5 SO SUBTRACT 5 FROM 2623

2623-5=2618

NOW FIND THE HIGHEST COMMON FACTOR OF 2002 AND 2618

which is 154

∴the greatest number that divides 2011 and 2623 leaves the remainder 9 and 5 respectively