as the product of the longest possible string of factors. Do not include 1 as a factor.

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1 Math Message Factors 1. Write all the pairs of factors whose product is 48. One pair has been done for you , 2. One way to write 36 as a product of factors is Another way is Write 36 as the product of the longest possible string of factors. Do not include 1 as a factor. Factor Trees and Greatest Common Factors One way to find all the prime factors of a number is to make a factor tree. First write the number. Underneath the number write any two factors whose product is that number. Then write factors of each of these factors. Continue until all the factors are prime numbers. Below are two factor trees for The greatest common factor of two whole numbers is the largest number that is a factor of both numbers. Example: Find the greatest common factor of 24 and 60. Step 1 List all the factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24. Step 2 List all the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Step 3 1, 2, 3, 4, 6, and 12 are on both lists. They are common factors. 12 is the largest number, so it is the greatest common factor of 24 and Find the greatest common factor of 18 and 27. Factors of 18: Factors of 27: Greatest common factor: 393

2 Factor Trees and Greatest Common Factors Another way to find the greatest common factor of two numbers is to use prime factorization. Example: Find the greatest common factor of 24 and 60. Step 1 Make factor trees and write the prime factorization of each number Step 2 Circle pairs of common factors. 24 2º2º2º3 60 2º2º3º5 Step 3 Multiply one factor in each pair of circled factors. The greatest common factor of 24 and 60 is 2 2 3, or Make a factor tree for each number below, and write the prime factorization. a. 10 b. 75 c

3 Factor Trees and Greatest Common Factors cont. 5. a. Which prime factor(s) do 10 and 75 have in common? b. What is the greatest common factor of 10 and 75? 6. a. Which prime factor(s) do 75 and 90 have in common? b. What is the greatest common factor of 75 and 90? 7. a. Which prime factor(s) do 10 and 90 have in common? b. What is the greatest common factor of 10 and 90? 8. Use the factor trees in Problem 4 to help you write each fraction below in simplest form. Divide the numerator and denominator by their greatest common factor. a b c What is the greatest common factor of 20 and 25? Write the fraction 2 in simplest form Use the space below to draw factor trees. What is the greatest common factor of 1,260 and 1,350? 395

4 Factor Trees and Least Common Multiples The least common multiple of two numbers is the smallest number that is a multiple of both numbers. Example: Find the least common multiple of 8 and 12. Step 1 List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, and so on. Step 2 List the multiples of 12: 12, 24, 36, 48, 60, and so on. Step 3 24 and 48 are in both lists. They are common multiples. 24 is the smallest number. It is the least common multiple for 8 and is also the smallest number that can be divided by both 8 and 12. Another way to find the least common multiple for two numbers is to use prime factorization. Example: Find the least common multiple of 8 and 12. Step 1 Write the prime factorization of each number: 8 2 º 2 º º 2 º 3 Step 2 Circle pairs of common factors. Then cross out one factor in each pair as shown below. 8 2 º 2 º º 2 º 3 Step 3 Multiply the factors that are not crossed out. The least common multiple of 8 and 12 is 2 º 2 º 2 º 3, or Make factor trees and write the prime factorizations for each number. a. 15 b. 9 c What is the least common multiple of a. 9 and 15? b. 15 and 30? c. 9 and 30? 396

5 Math Boxes 1. Solve. a. If 15 marbles are 3 of the marbles in a bag, how many are in the bag? marbles 5 b. If 14 pennies are 7% of a pile of pennies, how many are in the pile? pennies c. 75 students are absent today. This is 10% of the students enrolled at the school. How many students are enrolled at the school? students d. Tyesha paid $90 for a new radio. It was on sale for 3 4 of the regular price. What is the regular price of the radio? A scooter is on sale for 30% of the list price. The sale price is $84. What is the list price? 3. Write or. a b c d Solve. a. One orange One cube weighs as much as Xs. weighs as much as Xs e X b. 6X 4X One triangle One paper clip weighs as much as X. weighs as much as X

3.1 Factors and Multiples of Whole Numbers

Math 1201 Date: 3.1 Factors and Multiples of Whole Numbers Prime Number: a whole number greater than 1, whose only two whole-number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7,