Factors and Factor Trees

Warm Up State whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. 345 764 1,230 848 3, 5 2, 4 2, 3, 5, 6, 2, 4, 8

Example: Find the factors of 12. A number is a factor of another if it divides into that number with no remainder. Example: Find the factors of 12. 1, 2 ,3, 4, 6, and 12 are factors of 12.

A number that has exactly two factors, 1 and itself is called a prime number. Examples: 23 2 17

A number that has more than two factors is called a composite number. Examples: 33 100 12

Practice List the factors of 36. 2. List the factors of 30. Is 6 prime or composite? Is 11 prime or composite? 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 5, 6, 10, 15, 30 composite prime

Prime Factorization You can break down a composite number into prime factors. You can do this by making a factor tree.

Example 1: Find the prime factorization of 24 by using a factor tree. Use two factors of 24. Do not use 1 and 24 because 1 is neither prime nor composite. If a number is prime you are finished. If a number is composite you need to keep factoring until you have all prime factors. 2 12 6 2 2 3 Prime factorization is 23 x 3.

24 4 6 2 2 2 3 You can choose another pair of factors of 24 and you still end up with the same prime factorization.

Example 2: Find the prime factorization of 50 by using a factor tree. 10 5 2 5 The prime factorization is 2 x 52.

Find the prime factorization of each number. 45 32 Practice Find the prime factorization of each number. 45 32 32 x 5 25

Closure Explain why 1 is neither prime nor composite. It has exactly one factor. Not two or more than two factors.