Fractions and Decimals Lesson 1 Fractions and Decimals Greatest Common Factor

Warm-Up Write three multiplication problems that equal 20. Find the value of 3 × 5. Find the value of 6 × 7.

Greatest Common Factor Target: Find the greatest common factor (GCF) of a set of numbers.

Vocabulary Factors: Whole numbers that can be multiplied to get a product. Prime Number: A whole number that has only two possible factors (1 and itself). Composite Number: A number with more than two factors. Greatest Common Factor: The greatest factor that is common to all the numbers. Prime Factorization: A composite number written as a product of all its prime factors.

Example 1 Determine if 12 is a prime or composite number. List the pairs of numbers that have a product of 12. 1 × 12 2 × 6 3 × 4 12 × 1 6 × 2 4 × 3 List each factor once. 1, 2, 3, 4, 6, 12 There are more than two factors so 12 is composite.

Example 2 Team 1 36 Players Team 2 30 Players Two local teams went to soccer camp together. At the camp the teams were asked to split into equal amounts for cabin groups. The players did not want to room with players from other teams. The camp directors want the largest number possible in each cabin. How many players will be in each cabin? Team 1 36 Players Team 2 30 Players

Example 2 (continued) Write each number as a product of two factors until only prime numbers remain. Write the prime factorization of each number and highlight common factors. Find the product of the common factors. 3× 2 = 6 The GCF is 6.

Example 3 Reagan Middle School students were asked to sit in equal rows for the assembly. There were 98 sixth graders, 84 seventh graders and 112 eighth graders. The teacher did not want grade levels to sit together, but the rows were to be as wide as possible. How many students should sit in each row? Factors of 98: 1, 2, 7, 14, 49, 98 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 Highlight the common factors. The GCF is 14. Fourteen students should sit in each row.

Find the Greatest Common Factor List the factors for each number. Highlight the common factors. Identify the GCF (greatest common factor).

Exit Problems Find the GCF of 56 and 64. Gina wants to sell 49 chocolate chip cookies and 35 sugar cookies. She is going to sell them on plates with equal amounts on each plate. Each plate needs to hold the largest number of cookies without mixing types of cookies. How many cookies should Gina put on each plate?

Communication Prompt What is a real life situation in which you would need to find the greatest common factor?