Divisibility, Greatest common divisor

One of the distinctive properties of the set of integers, is that if you divide a positive number into any integer, you will get a  unique quotient and remainder.  More precisely, if you divide b () into a, there will be integers q and r such that and .     We will take this as given, but it can be proven by mathematical  induction.

If , i. e.,  ,  then all of the following say the same thing
            b divides a
            a is a multiple of b
            b is a factor of a
            b is a divisor of a

is the largest positive integer that is a divisor of both a and b.

In Mathematica you can get the gcd of two numbers using the function GCD:

More information can be obtained with ExtendedGCD

We'll see what the second item in this output represents below.