Divisibility test are tools to determine if a number can be divided by particular factor. While there are many numbers which are Prime (divisible by the number and 1 only), many more of the numbers we encounter are Composite (divisible by more than 2 numbers). By learning divisibility tests, a person can quickly determine whether (1) a number is composite or prime, (2) the numbers share factors (finding common denominators, LCD), (3) the GCF of a list of numbers, and many other short cuts in arithmetic.