4-1 Factors and Prime Factorization I CAN list all the factors of a number. I CAN write prime factorizations of composite numbers.

4-1 Factors and Prime Factorization Vocabulary factor prime factorization

4-1 Factors and Prime Factorization Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors = Factors Product 2 63 ÷ = 6÷2 = 3 6 is divisible by 3 and 2.

4-1 Factors and Prime Factorization When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring. Helpful Hint

4-1 Factors and Prime Factorization Example 1: Finding Factors List all of the factors of the number 16. A = = is a factor. 2 is a factor. 16 = is not a factor. 4 is a factor. 5 is not a factor. 6 is not a factor. 7 is not a factor. 16 = and 2 have already been listed so stop here. The factors of 16 are 1, 2, 4, 8, and You can draw a diagram to illustrate the factor pairs.

4-1 Factors and Prime Factorization Example 1: Finding Factors List all of the factors of the number 19. B = is not divisible by any other whole number. The factors of 19 are 1 and 19.

4-1 Factors and Prime Factorization You Try! Example 1 List all of the factors of the number 12. A The factors of 12 are 1, 2, 3, 4, 6, and 12 You can draw a diagram to illustrate the factor pairs.

4-1 Factors and Prime Factorization Try It! Example 1 List all of the factors of the number 11. B is not divisible by any other whole number. The factors of 11 are 1 and 11.

4-1 Factors and Prime Factorization You can use factors to write a number in different ways. Factorization of The prime factorization of a number is the number written as the product of its prime factors. Notice that these factors are all prime.

4-1 Factors and Prime Factorization You can use exponents to write prime factorizations. Remember that an exponent tells you how many times the base is a factor. Helpful Hint

4-1 Factors and Prime Factorization Example 2: Writing Prime Factorizations Method 1: Use a factor tree. Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor = = The prime factorization of 24 is , or Write the prime factorization of 24.

4-1 Factors and Prime Factorization Example 2: Writing Prime Factorizations Method 2: Use a ladder diagram. Choose a prime factor of 45 to begin. Keep dividing by prime factors until the quotient is = = The prime factorization of 45 is or Write the prime factorization of 45.

4-1 Factors and Prime Factorization In Example 2, notice that the prime factors may be written in a different order, but they are still the same factors. Except for changes in the order, there is only one way to write the prime factorization of a number.

4-1 Factors and Prime Factorization You Try! Example 2 Write the prime factorization of 28. A. Method 1: Use a factor tree. Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor = = The prime factorization of 28 is 2 2 7, or

4-1 Factors and Prime Factorization You Try! Example 2 Write the prime factorization of 36. B. Method 2: Use a ladder diagram. Choose a prime factor of 36 to begin. Keep dividing by prime factors until the quotient is = The prime factorization of 36 is , or =

4-1 Factors and Prime Factorization CAN YOU list all the factors of a number? CAN YOU find the prime factorization of a number?

4-1 Factors and Prime Factorization Lesson Quiz List all the factors of each number , 2, 4, 5, 8, 10, 20, 40 1, 2, 11, 22 1, 3, 17, 51 Write the prime factorization of each number  3  5

4-1 Factors and Prime Factorization HOMEWORK