In this lesson, we will learn

- prime numbers
- composite numbers
- why 1 is not a prime number

**What is a Prime Number?**

A **prime number** is a whole number that has exactly two factors, 1 and itself.

**For example**

The number 29 has exactly two factors, which are 1 and 29.

So, 29 is a prime number.

**The prime numbers up to 100 are**

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

We can use the Sieve of Eratosthenes to find all prime numbers up to any given limit.

The number 2 is the **only prime that is even**. All other even numbers have 2 as a factor and so they are composite numbers.

**Twin primes** are pairs of primes whose difference is 2.

(3, 5), (5, 7) and (11, 13) are examples of twin primes.

**What is a Composite Number?**

A number that has more than 2 factors is called a **composite number**.

**For example:**

The number 28 has six factors which are 1, 2, 4, 7, 14, and 28.

So, 28 is not a prime number. It is a composite numbers.

**Example:**

Determine whether each of the following number is prime.

a) 43

b) 57

**Solution:**

a) 43 is only divisible by 1 and 43. It is a prime number.

b) 57 ÷ 3 = 19. It is not a prime number.

**What are relatively prime numbers?**

When two composite numbers have no common factors (other than 1), they are said to be **relatively prime**. For example, the numbers 8 and 15 are relatively prime.

**How to identify prime numbers?**

**How to distinguish between prime numbers and composite numbers?**

A prime number is a number greater than 1, which is only divisible by 1 and itself.

**Recognizing prime and composite numbers**

Example:

Determine whether the following numbers are prime, composite or neither:

24, 2, 1, 17

No, the number **1 is not a prime number** because it has only one factor.

Another reason is related to the Fundamental Theorem of Arithmetic as explained in the following video.

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