Factors and Greatest 8-1 Common Factors Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1
Warm Up 1. 50, 6 2. 105, 7 3. List the factors of 28. no yes 1. 50, 6 2. 105, 7 3. 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 number no yes ±1, ±2, ±4, ±7, ±14, ±28 4. 11 prime 5. 98 composite; 49 2
Objectives Write the prime factorization of numbers. Find the GCF of monomials.
Vocabulary prime factorization greatest common factor
The whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. You can use the factors of a number to write the number as a product. The number 12 can be factored several ways. Factorizations of 12 1 12 2 6 3 4 1 4 3 2 2 3
Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor, or GCF. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 32: 1, 2, 4, 8, 16, 32 Common factors: 1, 2, 4 The greatest of the common factors is 4.
Example 2A: Finding the GCF of Numbers Find the GCF of each pair of numbers. 100 and 60 Method 1 List the factors. factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 List all the factors. factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Circle the GCF. The GCF of 100 and 60 is 20.
Check It Out! Example 2a Find the GCF of each pair of numbers. 12 and 16 Method 1 List the factors. List all the factors. factors of 12: 1, 2, 3, 4, 6, 12 Circle the GCF. factors of 16: 1, 2, 4, 8, 16 The GCF of 12 and 16 is 4.
You can also find the GCF of monomials that include variables You can also find the GCF of monomials that include variables. To find the GCF of monomials, write the prime factorization of each coefficient and write all powers of variables as products. Then find the product of the common factors.
Example 3A: Finding the GCF of Monomials Find the GCF of each pair of monomials. 15x3 and 9x2 Write the prime factorization of each coefficient and write powers as products. 15x3 = 3 5 x x x 9x2 = 3 3 x x Align the common factors. 3 x x = 3x2 Find the product of the common factors. The GCF of 3x3 and 6x2 is 3x2.
Example 3B: Finding the GCF of Monomials Find the GCF of each pair of monomials. 8x2 and 7y3 Write the prime factorization of each coefficient and write powers as products. 8x2 = 2 2 2 x x 7y3 = 7 y y y Align the common factors. There are no common factors other than 1. The GCF 8x2 and 7y is 1.
If two terms contain the same variable raised to different powers, the GCF will contain that variable raised to the lower power. Helpful Hint
Check It Out! Example 3a Find the GCF of each pair of monomials. 18g2 and 27g3 Write the prime factorization of each coefficient and write powers as products. 18g2 = 2 3 3 g g 27g3 = 3 3 3 g g g Align the common factors. 3 3 g g Find the product of the common factors. The GCF of 18g2 and 27g3 is 9g2.
Find the GCF of each pair of monomials. Check It Out! Example 3b Find the GCF of each pair of monomials. Write the prime factorization of each coefficient and write powers as products. 16a6 and 9b 16a6 = 2 2 2 2 a a a a a a 9b = 3 3 b Align the common factors. The GCF of 16a6 and 7b is 1. There are no common factors other than 1.
Check It Out! Example 3c Find the GCF of each pair of monomials. 8x and 7v2 Write the prime factorization of each coefficient and write powers as products. 8x = 2 2 2 x 7v2 = 7 v v Align the common factors. There are no common factors other than 1. The GCF of 8x and 7v2 is 1.
Lesson Quiz: Part II Find the GCF each pair of monomials. 5. 12x and 28x3 6. 27x2 and 45x3y2 7. Cindi is planting a rectangular flower bed with 40 orange flower and 28 yellow flowers. She wants to plant them so that each row will have the same number of plants but of only one color. How many rows will Cindi need if she puts the greatest possible number of plants in each row? 4x 9x2 17