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Name _____________________________________ Date ______________ Number Theory and Systems Greatest Common Factor Venn Diagram 5 3 5 A 2 3 B Venn Diagrams are used to illustrate similarities and differences between two or more objects. They can be used in math to represent similarities and differences between numbers as well. Each circle represents a composite number. Circle A represents the number 75 and includes the prime factors 3 and 5. Circle B represents the number 90 and includes the prime factors 2, 3, and 5. The numbers 3 and 5 in the center represent common factors of 75 and 90. The greatest common factor of 75 and 90 is the product of the common prime factors, 15. Refer to the Venn Diagram below to answer the following questions. 2 5 3 2 3 5 A. What are the two composite numbers? B. What is the prime factorization of each number? © 2003 CompassLearning, Inc. Activity 67115 Name _____________________________________ Date ______________ Number Theory and Systems Greatest Common Factor C. How did you determine the composite numbers? D. What is the greatest common factor of the two numbers? E. How did you use the Venn Diagram to find the greatest common factor? F. How would the Venn Diagram look if 250 were added as a third circle? G. What is the greatest common factor among the three numbers? H. List all of the common factors of 250, 300, and 450. How can you use the Venn diagram to find the common factors? © 2003 CompassLearning, Inc. Activity 67115 Name _____________________________________ Date ______________ Number Theory and Systems Greatest Common Factor Solve. I. The greatest common factor of two numbers is 30. Their least common multiple is 420. One of the numbers is 210. What is the other number? J. Denise is thinking of two numbers. Their greatest common factor is 6. Their least common multiple is 36. One of the numbers is 12. What is the other number? © 2003 CompassLearning, Inc. Activity 67115 Name _____________________________________ Date ______________ Number Theory and Systems Connections Think About It How can you use the greatest common factor to find the simplest form of a fraction? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ A Floral Arrangement A florist receives 45 daisies and 60 lilies. The florist charges $1 per daisy and $2 per lily. What are the different numbers of vases that will allow an equal distribution of flowers and how much will each cost? (Assume that the price of each vase is only based on the number and type of flowers used.) © 2003 CompassLearning, Inc. Activity 67115
