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Understanding Prime Factorization and Exponential Form of Numbers

Explore the concept of prime factorization and exponential form in this lesson. Learn how to find the prime factorization of numbers and use it to calculate the greatest common factor (GCF). Practice determining factors, multiples, and GCF through engaging activities and real-life problem-solving scenarios. Enhance your math skills by mastering these fundamental concepts.

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Understanding Prime Factorization and Exponential Form of Numbers

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  1. Warm-Up #3 Use the following terms to describe your number: prime factorization and exponential form. Underline these terms in your journal. Be sure to give an accurate description with numerical justifications.

  2. If a room’s area is 60 square feet, what are the possible combinations of dimensions (length and width)? • What is it asking? • Name all of the factor facts for 60. • 1 x 60 It could be 1 foot long and 60 feet wide. • 2 x 30 It could be 2 foot long and 30 feet wide. • 3 x 20 It could be 3 foot long and 20 feet wide. • 4 x 15 It could be 4 foot long and 15 feet wide. • 5 x 12 It could be 5 foot long and 12 feet wide. • 6 x 10 It could be 6 foot long and 10 feet wide.

  3. 4-2 Factors and Prime Factorization Course 1 Insert Lesson Title Here Lesson Quiz List all the factors of each number. 1. 22 2. 40 3. 51 1, 2, 11, 22 1, 2, 4, 5, 8, 10, 20, 40 1, 3, 17, 51 Write the prime factorization of each number. 4. 32 5. 120 25 23 3  5

  4. Factors and Multiples Number Theory GONE WILD! Factors “Fit” into Families Multiples Multiply like Rabbits!

  5. What am I Learning Today? GCF How will I show that I learned it? Show how prime factorization can be used to find GCF Determine the GCF between two sets of data

  6. Vocabulary Common factor: Factors shared by two or more whole numbers Greatest Common Factor (GCF): The largest number that divides two or more numbers evenly.

  7. What are common factors? Factors shared by two or more whole numbers Questions Answers What is the largest of the common factors? The greatest common factor, or GCF. How do I find the GCF? Using the list method or the ladder How do I use the list method? 1. List all the factor pairs for those two numbers. 2. Circle the largest factor that they share. List the GCF for 28 and 42 Factors of 28: Factors of 42: 1, 2, 4, 7, 14, 28 1, 2, 3, 6, 7, 14, 21, 42 The GCF of 28 and 42 is 14. • Begin with a factor that divides into each number evenly. Does not have to be prime. • Keep dividing until there are no more common factors. • 3. Find the product of the numbers you divided by (GCF IS ON THE LEFT). How do I use the ladder method?

  8. Using the ladder, find the GCF for 40 and 16. Questions Answers 2 40 16 2• 2•2= 8 2 20 8 2 10 4 The GCF of 40 and 16 is 8 5 2

  9. Find the Greatest Common Factor Use BOTH the list and ladder method in order to check your answers. Factors of 32: 1, 2, 4, 8, 16, 32 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF of 32 and 24 32 24 2 16 12 2 8 6 2 4 3 GCF of 54 and 36 54 36 2 Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 27 18 3 9 6 3 3 2

  10. Find GCF using a Venn Diagram

  11. Paired Discussion Turn to a partner and discuss the following: What is the GCF of two prime numbers? Explain. Each prime number only has two factors, so they can ONLY share the number ONE.

  12. GCF Problem Solving How can you tell if a word problem requires you to use Greatest Common Factor?

  13. If it is a GCF Problem You are probably being asked: Do we have to split things into smaller sections? Are we trying to figure out how many people we can invite? Are we trying to arrange something into rows or groups?

  14. GCF Example: Applying what we have learned… Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? • K: The pieces of cloth are 72 and 90 inches wide. • W: How wide should she cut the strips so that they are the largest possible equal lengths. • L: This problem can be solved using Greatest Common Factor because we are cutting or “dividing” the strips of cloth into smaller pieces (factor) of 72 and 90.

  15. When is this useful? Dr. Doyle’s band students have been invited to march in a parade along with another school. Since one band marches directly behind another, all the rows must have the same number of students. Dr. Doyle had 36 students and the other band has 60 students. What is the greatest number of students who can be in each row? 12 students per row

  16. Consumer Application Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make? HINT: The answer will be the greatest number of fruit baskets 18 oranges and 27 pears can form so that each basket has the same number of oranges, and each basket has the same number of pears. The GCF of 18 and 27 is 9.

  17. Question #1 Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest number of students she can have in her class so that each student gets an equal number of crayons and an equal number of paper? GCF: 30 students

  18. Question #2 Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use? GCF: 8 inch tile

  19. Question #3 I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row? GCF: 10 trees

  20. Ticket Out The Door • Find the GCF for the following problems. • 12 and 15 • 16, 28, and 48

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