Divisors

Number Theory Level 3

When a positive integer n n is divided by 3 , 4 , 5 , 6 , 7 3, 4, 5, 6, 7 , it gives the remainders 2 , 3 , 4 , 5 , 6 2, 3, 4, 5, 6 respectively. Find the LEAST n n .


The answer is 419.

William Isoroku by William Isoroku , 25, USA

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.

3 solutions

Kenny Lau
Nov 30, 2014

To avoid ambiguity I would suggest you to include the assumption that n is positive, since -421 satisfies your condition and is smaller than the answer 419.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Arun Ar
Jul 22, 2014

smallest number would be LCM of Divisors - constant difference between Divisors and Remainders

constant difference between Divisors and Remainders = 1 ie, 3-2=1, 4-5=1

smallest number = LCM of 3,4,5,6 - 1 = 420 - 1 = 419

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Akash Saini
Jul 21, 2014

First take the LCM of 3,4,5,6 that would be 420. So now see there is a common ration between quotient and remainder in each case is 1. 3-2=1, 4-5=1 so now subtract 1 from LCM 420 now that no. Would be 419

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...