Homework Help Forum: Pre-Calculus IB

Posted by Steve Jobs on Sunday, October 25, 2009 at 8:15pm.

If R is the remainder when each of the numbers 1059, 1417, and 2312 is divided by D, where D is an integer greater than 1, compute the value of D - R.

• Pre-Calculus IB - MathMate, Sunday, October 25, 2009 at 9:49pm

  Let p,q,r,s,t be some arbitrary integers, then A=1059 = pD+R B=1417 = qD+R C=2312 = rD+R E = B-A = sD = 358 = 2*179 F = C-B = tD = 895 = 5*179 Using Euclid's algorithm, all common factors between E and F are also common factors of (A-R),(B-R) and (C-R). Thus 179 is the (only) common factor between the three numbers (A-R), (B-R) and (C-R), from which we determine that D=179 and R=164. D-R=179-164=15.

  
  

• Pre-Calculus IB - Tiffany, Sunday, October 25, 2009 at 9:52pm

  1417-1059=358=2*179 2312-1417=895=5*179 D=179 R=164 D-R=15

  
  

Answer this Question

First Name:
School Subject:
Answer:

For Further Reading