BolkowN

2020-10-28

a.)Explain in your own words what this problem is asking.
b.)Explain the meaning of any notation used in the problem and in your solution.
c.)Describe the mathematical concept(s) that appear to be foundational to this problem.
d.)Justified solution to or proof of the problem.
Find the greatest common divisior of a,b, and c and write it in the form ax+by+cz for integers x,y, and z.
a=26,b=52,c=60

### Answer & Explanation

Khribechy

Step 1
Consider the following information:
a=26,b=52,c=60
Greatest common divisor of 60 and 52:
$60=52×1+8$ ...(1)
$52=8×6+4$ ...(2)
$8=4×2+0$ ...(3)
Greatest common divisor of 60 and 52 is 4.
Greatest common divisor of 26 and 4:
$26=4×6+2$ ...(4)
$4=2×2+0$ ...(5)
Greatest common divisor of 26 and 4 is 2.
Step 2
From equation (4):
$2=26-4×6$
From equation (2):
$2=26\left(52-8×6\right)×6$
$2=26-52×6+8×36$
From equation (1):
$2=26-52×6+\left(60-52×1\right)×36$
$2=26-52×6+60×36-52×36$
2=26(1)+(-42)52+(36)60
Hence, the solution is x=1,y=-42, z=36.

Do you have a similar question?

Recalculate according to your conditions!