When a Pythagorean triple consists of natural numbers which are relatively prime, it is more properly labeled a primitive Pythagorean triple.

Consider both pythagorean triples (3, 4, 5) and (6, 8, 10).

(3, 4, 5) IS a primitive Pythagorean triple since there is no natural number (other than 1) which divides evenly into all three numbers 3, 4 and 5.

(6, 8, 10) IS NOT a primitive Pythagorean triple since the natural number 2 divides evenly into all three numbers 3, 4 and 5.