4-2 Factors and Prime Factorization Course 1 Lesson Presentation Lesson Presentation

Learn to write prime factorizations of composite numbers. Course Factors and Prime Factorization

Vocabulary factor prime factorization Insert Lesson Title Here Course Factors and Prime Factorization

Course 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.

Course 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

Course Factors and Prime Factorization Additional Example 1A: Finding Factors List all factors of 16. Begin listing factors in pairs. 16 = = 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.

Course Factors and Prime Factorization Additional Example 1B: Finding Factors List all factors of 19. Begin listing all factors in pairs. 19 = is not divisible by any other whole number. The factors of 19 are 1 and 19.

Course Factors and Prime Factorization Check It Out: Example 1A List all factors of 12. Begin listing factors in pairs. 12 = = is a factor. 2 is a factor. 3 is a factor. 4 and 3 have already been listed so stop here. 12 = The factors of 12 are 1, 2, 3, 4, 6, and = 3 4 You can draw a diagram to illustrate the factor pairs.

Course Factors and Prime Factorization Check It Out: Example 1B List all factors of 11. Begin listing all factors in pairs. 11 = is not divisible by any other whole number. The factors of 11 are 1 and 11.

Course 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.

Course 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

Course Factors and Prime Factorization Additional Example 2A: 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.

Course Factors and Prime Factorization Additional Example 2B: 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.

Course 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.

Course Factors and Prime Factorization Check It Out: Example 2A Write the prime factorization of 28. 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

Course Factors and Prime Factorization Check It Out: Example 2B Write the prime factorization of 36. 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 =

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