Question

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

Answer 1

SOLUTION:

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

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Hey there !!

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


→ Solution :-)


➡Clearly, the required number divides ( 2011 - 9 ) = 2002 and ( 2623 - 5 ) = 2618 exactly.


=> Required number = HCF ( 2002 , 2618 ).


▶Now, 2002 = 2 × 7 × 11 × 13.

And, 2618 = 2 × 7 × 11 × 17.


=> HCF ( 2002 , 2618 ) = Product of common terms .

=> HCF ( 2002 , 2618 ) = 2 × 7 × 11 .


$\huge \boxed{ = 154. }$



✔✔Hence, the greatest number is 154. ✅✅

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