Problem 3

Number Theory Level 3

Certain divisor gives remainder 8, 9 and 4 when numbers 242, 698 and 940 respectively are divided by it. The value of divisor is

12 13 14 11

Sanjay Balaji by Sanjay Balaji , 21, India

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3 solutions

Sanjay Balaji
Apr 7, 2014

Let it be k, 242 = nk + 8, 698 = mk + 9, 940 = lk + 4. Solve for k

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Rahma Anggraeni
May 19, 2014

242 − 8 = 234 242-8=234

698 − 9 = 689 698-9=689

940 − 4 = 936 940-4=936

Then try one of them, 234 234 can only be divided by 13 13 so the answer is 13 \boxed{13}

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Raviteja Deekonda
Apr 11, 2014

subtract reminder form each dividend n compute l.C.M

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