Prime or composite

Key notes:

What are Prime Numbers?

Definition: A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.

Examples:

• 2: Divisors are 1 and 2.
• 5: Divisors are 1 and 5.
• 13: Divisors are 1 and 13.

What are Composite Numbers?

Definition: A composite number is a natural number greater than 1 that has more than two distinct positive divisors.

Examples:

• 4: Divisors are 1, 2, 4.
• 6: Divisors are 1, 2, 3, 6.
• 9: Divisors are 1, 3, 9.

Identifying Prime and Composite Numbers

Prime Numbers:

• Characteristics: Only divisible by 1 and the number itself.
• Visual Aid:
  • Example: 7 can only be divided by 1 and 7.

Composite Numbers:

• Characteristics: Can be divided by numbers other than 1 and itself.
• Visual Aid:
  • Example: 8 can be divided by 1, 2, 4, and 8.

Prime vs. Composite Chart

• Chart:

Number	Prime or Composite?	Divisors
2	Prime	1, 2
4	Composite	1, 2, 4
5	Prime	1, 5
6	Composite	1, 2, 3, 6
7	Prime	1, 7
8	Composite	1, 2, 4, 8
9	Composite	1, 3, 9
11	Prime	1, 11

How to Find Out If a Number is Prime or Composite

Steps:

1. List Divisors:
   • Check numbers from 2 up to the square root of the number.
2. Check Divisibility:
   • If you find a divisor other than 1 and the number itself, it is composite.
3. Example:
   • Check if 17 is prime:
     • Divisors to check: 2, 3, 4
     • 17 is not divisible by these, so it’s prime.

Prime Number Chart (Small Prime Numbers)

• Chart:

1	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

Fun Facts about Prime and Composite Numbers

• Fact 1: 2 is the only even prime number.
• Fact 2: Every composite number can be expressed as a product of prime numbers (prime factorization).

Prime Factorization

Definition: Breaking down a composite number into its prime factors.

Example:

• 24 can be factored into 2 x 2 x 2 x 3.
• Visual Aid:
  • Explanation: 24 = 2³ x 3

let’s practice!