A number theory problem by Michael Wu

Number Theory Level 1

When 242 is divided by a certain divisor, the remainder obtained is 8 . When 698 is divided by the same divisor, the remainder obtained is 9 . However, when the sum of 242 and 698 is divided by the divisor, the remainder obtained is 4 . What is the value of the divisor?

15 12 14 13

Michael Wu by Michael Wu , 23, Indonesia

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2 solutions

Sunil Pradhan
Jul 6, 2014

242 ÷ No. remainder 8, and 698 ÷ No. remainder 9

means if remainder is subtract from dividend

it means (242 – 8 = 234) and (698 – 9 = 689) is divisible by required number and such number is GCD of 234 and 689

which is 13

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Let the divisor is x.
242 x \frac{242}{x} the remainder is 8. So, (242-8)=234 can be divided by x.
698 x \frac{698}{x} the remainder is 9. So, (698-9)=689 can be divided by x.
The only solution so that both of 234 and 689 can be devided by x, is x=13


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