Question

When each of 702, 787, and 855 is divided by the positive integer m, the remainder is always the positive integer r. When each of 412, 722, and 815 is divided by the positive integer n, the remainder is always the positive integer s r. Find m+n+r+ s.

Answer 1

take difference of two no.s at a time,

787-702=85 and

855-787=68

clearly we can see that hcf of 85 and 68 is 17.

dividing all three no.s will give 5 as remainder

therefore, m=17 and r=5.

similarly, 815-722=93 and 722-412=310

hcf of 93 and 310 is 31. dividing all three no.s will give 9 as remainder, hence n=31 and s=9.

m+n+r+s=17+31+5+9 =62