Warmup List the factors for the following numbers

Warm-up List the factors for the following numbers: 1. 30 1, 2, 3, 5, 6, 10, 15, 30 2. 66 1, 2, 3, 6, 11, 22, 33, 66 3. 71 1, 71

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What am I Learning Today? Factors Prime Factorization How will I show that I learned it? Apply factors Decompose Numbers into their Prime Factorization

Vocabulary Prime Factorization: A number written as the product of its prime factors. Exponent: Tells how many times a number (the base) is used as a factor.

You can use factors to write a number in different ways. Factorization of 12 1 • 12 2 • 6 3 • 4 3 • 2 Notice that these factors are all prime. What do you notice about how the last set of factors are written? The prime factorization of a number is the number written as the product of its prime factors.

What is an exponent? An exponent tells how many times a number called the base is used as a factor. A number is in exponential form when it is written with a base and an exponent. Exponent Base 3 = 7 7 7= 343 7

To decompose a number into its prime factorization, you may use the tree or the ladder method.

Write the prime factorization of 24 (using a factor tree) Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor. 24 2 • 6 12 • 6 2 • 3 3 • 2 4 2 • 2 24 = 3 • 2 • 2 24 = 2 • 2 • 3 The prime factorization of 24 is 2 • 2 • 3

To write your answer using exponents The prime factorization of 24 is 2 • 2 • 3 3 2 • 3

Write the prime factorization of 24 (using a ladder) Choose a prime factor of 24 to begin. Keep dividing by prime factors until the quotient is 1. 2 24 2 3 24 12 2 8 2 6 2 3 3 1 24 = 2 • 2 • 3 4 2 2 1 24 = 3 • 2 • 2 The prime factorization of 24 is 2 • 2 • 3

To write your answer using exponents The prime factorization of 24 is 2 • 2 • 3 3 2 • 3

Practice Tree Method 45 Ladder Method

Practice Tree Method 120 Ladder Method

Practice Tree Method 72 Ladder Method

Practice Tree Method 48 Ladder Method

Groups Go to the color of your group. Each person must be able to factor all problems in your clip to prime factors using both the ladder method and the tree method. When time is called, a member of your group will be called to the front to factor one of your problems to primes using one of the methods. You don’t know which member You don’t know which problem You don’t know which method