Presentation on theme: "Factors and Greatest 7-1 Common Factors Warm Up Lesson Presentation"— Presentation transcript:
1Factors and Greatest 7-1 Common Factors Warm Up Lesson Presentation Lesson QuizHolt McDougal Algebra 1Holt Algebra 1
2Warm Up 1. 50, 6 2. 105, 7 3. List the factors of 28. 4. 11 5. 98 1. 50, , 73. List the factors of 28.Tell whether each number is prime or composite. If the number is composite, write it as the product of two numbers.Tell whether the second number is a factor of the first number4. 115. 98
3Objectives Write the prime factorization of numbers. Find the GCF of monomials.
4Factors: numbers that are multiplied to find a product. *A number is divisible by its factors.Example:12 can be factored several ways. How??Factorizations of 121 122 63 4
5Prime factorization: factoring a number into only prime numbers. *Only one way to write the prime factorization of a number.Factorizations of 121 122 63 4
6Example 1: Writing Prime Factorizations Write the prime factorization of 98 and 25.Factor treea. 98b. 25Choose any two factorsof 98 to begin. Keep finding factors until each branch ends in a prime factor.259825 = 5 5The prime factorization of 25 is 5 5 or 52.98 =The prime factorization of 98 is 2 7 7 or 2 72.
7Check It Out! Example 1Write the prime factorization of each number.a. 40b. 33c. 19
8Common Factors: factors shared by two or more whole numbers. Greatest common factor (GCF): largest common factor between two or more numbersFactors of 12:1, 2, 3, 4, 6, 12Factors of 32:1, 2, 4, 8, 16, 32Common factors: 1, 2, 4The greatest of the common factors is 4.
9Example 2A: Finding the GCF of Numbers Find the GCF of each pair of numbers.100 and 60Method 1 List the factors.factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100List all the factors.factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60Circle the GCF.The GCF of 100 and 60 is 20.
10Example 2B: Finding the GCF of Numbers Find the GCF of each pair of numbers.26 and 52Method 2 Prime factorization.Write the prime factorization of each number.26 = 1352 = 2 2 13Align the common factors.2 13 = 26The GCF of 26 and 52 is 26.
11Check It Out! Example 2aFind the GCF of each pair of numbers.12 and 16Method 1 List the factors.
12Check It Out! Example 2bFind the GCF of each pair of numbers.15 and 25Method 2 Prime factorization.
13Steps to find the GCF of monomials with variables Write the prime factorization of each coefficientWrite all powers of variables as products.Find the product of the common factors.
14Example 3A: Finding the GCF of Monomials Find the GCF of each pair of monomials.15x3 and 9x2Write the prime factorization of each coefficient and write powers as products.15x3 = 3 5 x x x9x2 = 3 3 x xAlign the common factors.3 x x = 3x2Find the product of the common factors.The GCF of 15x3 and 9x2 is 3x2.
15Example 3B: Finding the GCF of Monomials Find the GCF of each pair of monomials.8x2 and 7y3Write the prime factorization of each coefficient and write powers as products.8x2 = 2 2 2 x x7y3 = y y yAlign the common factors.There are no common factors other than 1.The GCF 8x2 and 7y3 is 1.
16Check It Out! Example 3aFind the GCF of each pair of monomials.18g2 and 27g316a6 and 9b
17Example 4: ApplicationA cafeteria has 18 chocolate-milk cartons and 24 regular-milk cartons. The cook wants to arrange the cartons with the same number of cartons in each row. Chocolate and regular milk will not be in the same row. How many rows will there be if the cook puts the greatest possible number of cartons in each row?The 18 chocolate and 24 regular milk cartons must be divided into groups of equal size. The number of cartons in each row must be a common factor of 18 and 24.
18Example 4 ContinuedFind the common factors of 18 and 24.Factors of 18: 1, 2, 3, 6, 9, 18Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24The GCF of 18 and 24 is 6.The greatest possible number of milk cartons in each row is 6. Find the number of rows of each type of milk when the cook puts the greatest number of cartons in each row.
19Example 4 Continued18 chocolate milk cartons6 containers per row= 3 rows24 regular milk cartons= 4 rowsWhen the greatest possible number of types of milk is in each row, there are 7 rows in total.
20#18-24(evens), 25-36(all), 40, 41, 57, and 58, skip 30 HOMEWORKPG#18-24(evens), 25-36(all), 40, 41, 57, and 58, skip 30