A positive integer is a number greater than zero that can be expressed without using a fraction. Five, 72 and 100,000 are all examples of positive integers.
Positive integers are sometimes called "counting numbers" because they are the numbers that most people use when they first learn how to count: one, two, three, etc. "Natural numbers" or "whole numbers" refers to all of the positive integers and also zero. Negative integers are numbers that can be expressed without using a fraction but that have a value of less than zero, such as -1. Zero is an integer, but is considered neither positive nor negative.