Number operations and integers Study Guide

A prime number is a whole number greater than 1 that has exactly two distinct positive divisors: 1 and itself. This means that a prime number cannot be divided evenly by any other whole number apart from 1 and its own value. For example, 7 is a prime number because it can only be divided by 1 and 7 without leaving a remainder. Numbers like 4 are not prime because they can be divided by 1, 2, and 4 (more than two divisors). It's very important to remember that 1 is not a prime number because it only has one divisor (itself), not two distinct divisors. The number 2 is unique as the only even prime number; all other even numbers are divisible by 2 and therefore have at least three divisors (1, 2, and themselves). Identifying prime numbers often involves testing divisibility by smaller prime numbers such as 2, 3, 5, 7, and so on. Understanding prime numbers is fundamental in many areas of mathematics, including factorisation, number theory, and cryptography.

A prime number is a whole number greater than 1 that has exactly two distinct positive divisors: 1 and itself. This definition is crucial. For example, 7 is a prime number because it can only be divided by 1 and 7 without leaving a remainder. Numbers like 4 are not prime because they can be divided by 1, 2, and 4 (more than two divisors). It's important to remember that the number 1 is not considered a prime number because it only has one divisor (itself), not two distinct divisors as required by the definition. The number 2 is the only even prime number; all other even numbers are divisible by 2, and thus have more than two divisors (1, 2, and the number itself, at least). To determine if a number is prime, you can test for divisibility by smaller prime numbers (2, 3, 5, 7, etc.) up to the square root of the number in question. If no such prime factor is found, the number is prime. For instance, to check if 29 is prime, we test divisibility by 2, 3, 5. We don't need to go further than 5 because the next prime, 7, has 7*7 = 49, which is greater than 29. Since 29 is not divisible by 2, 3, or 5, it is a prime number.