Divisors

Number Theory Level 2

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


The answer is 13.

Shreya R by Shreya R , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

5 solutions

according to problem 242-8 = 234 is divisible by x . 698-9 = 689 is divisible by x . 242+698= 940-4 = 936 is divisible by x . therefore.... 936-689 = 247 is divisible by x . 247-234 = 13 is divisible by x . Since 13 is a prime number x = 13..

5 Helpful 0 Interesting 0 Brilliant 0 Confused

easiest way will be to find a number which when divide 17(remainder of 242 + remainder of 698) to get the remainder as 4. the only number exist is 13

prashant khulbe - 7 years, 1 month ago

But when divided by 13 there is ni relevant answer

Lokesh sharama - 6 years, 10 months ago
Satvik Golechha
Mar 29, 2014

The answer is gcd(242-6, 698-9, 242+698-4), that is 13.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Since 242-8 =234 is fully divisible and similarly 689 is too. So 234+689 is fully divisible so no remainder. but for {(234+8) + ( 689+9)}/2 remainder should be 17 but actually it is 4 so 17-4 = 13 is divisor.

Narendra Jakhar - 7 years, 1 month ago

more detailed

Irfan Shah - 7 years, 1 month ago
Barr Shiv
Dec 11, 2018

we know that (8+9)mod N=4 and N>9 therefore the only option is 13

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Lenard Arceo
Jun 24, 2014

According to the problem, 234 dividend must be the exact number in the first, in the second, 689 must be the exact dividend, and in the third, 238 must be the exact dividend, so the greatest common divisor of 234 and 689 is 13.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mark Kong
Jun 3, 2014

From the first two facts alone, we get 234 and 689 are multiples of the divisor. 689 is not divisible by 2 or 3 by the divisibility tests, so we can divide 234 by 18 to get 13. Therefore, 13 must be the answer because the only other common divisor of 234 and 689 is 1, but you cannot get a remainder of 8 when dividing by 1.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...