Factoring Integers Chapter 5 Section 5.1

Objective Students will factor integers and find the greatest common factor of several integers.

Vocabulary Factor Factor set Prime Prime factorization Greatest common factor (GCF)

Concept When you write 56 = 8 * 7 or 56 = 4 * 14, you have factored 56. In the first case, 8 and 7 are the factors. In the second case the factors are 4 and 14. To factor a number over a given set, you write it as a product of numbers in that set, called the factor set.

Concept You can find the positive factors of a given positive integer by dividing it by positive integers in order. Record only the integral factors. Continue until a pair of factors is repeated.

Example Give all positive factors of 56

Example Give all the positive factors of 88

Concept A prime number, or prime, is an integer greater than 1 that has no positive integral factor other than itself and 1. The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 To find the prime factorization of a positive integer, you express is as a product of primes. You will use a factor tree to find the prime numbers.

Concept Exponents are generally used for prime factors that occur more than once in a factorization. The prime factorization of an integer is unique (there is only one) except for the order of the factors.

Find the prime factorization of 120 Example Find the prime factorization of 120

Find the prime factorization of 200 Example Find the prime factorization of 200

Concept A factor of two or more integers is called a common factor of the integers. The greatest common factor (GCF) of two or more integers is the greatest integer that is a factor of all the given integers.

Concept To find the greatest common factor (GCF) you must first find the prime factorization of each integer. Then form the product of the smaller powers of each common prime factor.

Example Find the GCF of 66 and 90

Example Find the GCF of 88 and 128

Questions

Assignment Worksheet