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

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Presentation on theme: "4-1 Factors and Prime Factorization I CAN list all the factors of a number. I CAN write prime factorizations of composite numbers."— Presentation transcript:

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

2 4-1 Factors and Prime Factorization Vocabulary factor prime factorization

3 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. 23 6 = Factors Product 2 63 ÷ = 6÷2 = 3 6 is divisible by 3 and 2.

4 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

5 4-1 Factors and Prime Factorization Example 1: Finding Factors List all of the factors of the number 16. A. 16 16 = 1 16 16 = 2 8 1 is a factor. 2 is a factor. 16 = 4 4 3 is not a factor. 4 is a factor. 5 is not a factor. 6 is not a factor. 7 is not a factor. 16 = 8 2 8 and 2 have already been listed so stop here. The factors of 16 are 1, 2, 4, 8, and 16. 1244168 You can draw a diagram to illustrate the factor pairs.

6 4-1 Factors and Prime Factorization Example 1: Finding Factors List all of the factors of the number 19. B. 19 19 = 1 19 19 is not divisible by any other whole number. The factors of 19 are 1 and 19.

7 4-1 Factors and Prime Factorization You Try! Example 1 List all of the factors of the number 12. A. 12 1243126 The factors of 12 are 1, 2, 3, 4, 6, and 12 You can draw a diagram to illustrate the factor pairs.

8 4-1 Factors and Prime Factorization Try It! Example 1 List all of the factors of the number 11. B. 11 11 is not divisible by any other whole number. The factors of 11 are 1 and 11.

9 4-1 Factors and Prime Factorization You can use factors to write a number in different ways. Factorization of 12 2 61 123 43 2 2 The prime factorization of a number is the number written as the product of its prime factors. Notice that these factors are all prime.

10 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

11 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. 24 212 6 2 2 3 24 6 4 322 2 24 = 2 2 2 3 24 = 3 2 2 2 The prime factorization of 24 is 2 2 2 3, or 2 3 3. Write the prime factorization of 24.

12 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 1. 345 3 1 15 5 5 45 = 3 3 5 545 3 1 9 3 3 45 = 5 3 3 The prime factorization of 45 is 3 3 5 or 3 2 5. Write the prime factorization of 45.

13 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.

14 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. 28 214 72 28 7 4 2 2 28 = 2 2 7 28 = 7 2 2 The prime factorization of 28 is 2 2 7, or 2 2 7.

15 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 1. 336 2 1 12 6 2 36 = 3 2 2 3 The prime factorization of 36 is 3 2 2 3, or 2 2 3 2. 336 3 1 12 2 4 36 = 3 3 2 2 3 3 2 2

16 4-1 Factors and Prime Factorization CAN YOU list all the factors of a number? CAN YOU find the prime factorization of a number?

17 4-1 Factors and Prime Factorization Lesson Quiz List all the factors of each number. 1. 22 2. 40 3. 51 1, 2, 4, 5, 8, 10, 20, 40 1, 2, 11, 22 1, 3, 17, 51 Write the prime factorization of each number. 4. 32 5. 120 2525 2 3  3  5

18 4-1 Factors and Prime Factorization HOMEWORK


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