Question

Find the largest number that divides 2011 and 2623 leaving remainders 9 and 5 respectively.


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Answer 1

Answer:

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Answer 2

Answer:

Let n divides 2011, 2623 leaving the remainder 9, 5 respectively.

The, 2011 can be expressed as,

2011=n p+9

n p=2011−9=2002

n p=2×7×11×13

And, 2623 can be expressed as,

2623=n q+5

n q=2623−5=2618

n q=2×7×11×17

But n should have the same value in both instances.

∴n=2×7×11

⟹p=13, q=17

Thus the number is,

n=2×7×11=154

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