**A positive integral factor is the factor of an integer that is both positive and divides evenly into another integer.** The definition of the set of integers is that it includes 0, the counting numbers and their opposites or negatives.

An example of a positive integral factor would be 12 for the integer 36. However, there are other positive integral factor for 36 that include 1, 2, 3, 4, 6, 9, 18 and 36. An application of finding integral factors in math is prime factorization. This entails finding the prime factors of an integer like 36, which is 2 x 2 x 3 x 3. This can also be given in exponential form as 2^{2} x 3^{2}.