A triple (x,y,z) of natural numbers is called a Primitive Pythagorean Triple (PPT) if it satisfies two conditions: (1) x[squared] + y[squared] = z[squared]; and (2) x, y, and z have no common factor other than one. All the PPT's are given by the parametric equations: (1) x = m[squared] - n[squared]; (2) y = 2mn; and (3) z = m[squared] + n[squared], where m and n are relatively prime natural numbers, not both odd, and m greater than n. As a result of the constraints imposed on m and n, x will be an odd number, y will be an even number of the form 4l, and z will be an odd number of the form 4k + 1. This article will address the following questions: (1) How many PPT's have the same x?; (2) How many PPT's have the same y?; and (3) How many PPT's have the same z?. As this article will show, the answers depend on the prime factorization of x, y, and z, respectively.