Greatest Common Divisor

Greatest Common Divisor List all the positive divisors of the following. 20 40 1 20 1 40 Make a list! 2 10 2 20 4 5 4 10 5 8

Greatest Common Divisor To find divisors of a number make a list starting with the lowest possible factor which is 1. We start with 1 and work our way up. We know we didn’t miss any factors because our list is organized.

Greatest Common Divisor When two numbers have the same divisor it is called a common divisor. Can you think of a common divisor for 12 and 6? 1, 2, 3 or 6

Greatest Common Divisor GCD- Largest number that divides evenly into a given set of numbers. Greatest Common Divisor- It is useful to know this for reducing fractions. There are two ways to find the GCD

Greatest Common Divisor Method # 1 List all the divisors of both numbers. Then find the greatest common divisor. Divisors of 12 1 x 12 2 x 6 3 x 4 Divisors of 30 1 x 30 2 x 15 3 x 10 5 x 6 Ex. Common Divisors are 1,2,3,6 GCD= 6

Make a List Greatest Common Divisor 60 84 This method is only useful if both numbers are small 1 60 1 84 2 30 2 42 3 20 3 28 4 15 4 21 5 12 6 14 6 10 7 12 GCD = 12

Greatest Common Divisor Method #1 is great, but you have to list all of the divisors for both numbers! This can sometimes take a while! That’s why there is Method # 2

Greatest Common Divisor Find the prime factorization of the two numbers. Then multiply their common factors. 12 30 2 6 2 15 2 3 3 5 2 and 3 Divisors the 2 numbers have in common are: Multiply the common factors. GCD = 2 x 3 = 6

Greatest Common Divisior Prime Factorization 60 84 2 30 2 42 2 15 2 21 3 5 3 7 GCD = 2 x 2 x 3=12

Greatest Common Divisor Prime Factorization 20 24 2 10 2 12 2 5 2 6 2 3 GCD = 2 x 2 = 4

GCD= 6 Common Divisors are 1,2,3,6 GCD, Make a List Method #1 GCD is the largest number that is a divisors of 2 numbers. It is useful to know this for reducing fractions. Step 1: List all the divisors of both numbers. Step 2: Then find the greatest common divisor. Divisors of 12 1 x 12 2 x 6 3 x 4 Divisors of 30 1 x 30 2 x 15 3 x 10 5 x 6 Ex. GCD= 6 Common Divisors are 1,2,3,6 This method is only useful if both numbers are small

Step 1: Find the prime factorization of the 2 numbers. Step 2: Then multiply their common factors. 12 30 2 6 2 15 2 3 3 5 Factors the 2 numbers have in common are: 2 & 3 Multiply the common factors. GCD = 2 x 3 = 6

Try these Find GCD of 30 and 75 Find GCD of 42 and 105