Find the largest number that divides 2011 and 2623 leaving remainders 9 and 5 respectively.
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Find the largest number that divides 2011 and 2623 leaving remainders 9 and 5 respectively.
please answer these question.....
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Answer:
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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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