How Do You Find the Greatest Common Factor of Two Numbers Using Prime Factorization?

36 can be broken down into 4 times 9
4 is 2 times 2 & 9 is 3 times 3
54 can be broken down into 6 times 9
6 is 2 times 3 & 9 is 3 times 3
One 2 is found in the prime factorizations of both 36 and 54
Two 3's are found in the prime factorizations of both 36 and 54
Multiplying the shared prime factors together should give us the greatest common factor
2 • 3 • 3 = 18

1. A prime number is a number whose only factors are 1 and itself
1. A prime number is a number whose only factors are 1 and itself
2. 4 • 9 = 36
3. Unfortunately, neither 4 nor 9 are prime
1. A prime number is a number whose only factors are 1 and itself
2. 2 • 2 = 4
3. 2 is a prime number
1. A prime number is a number whose only factors are 1 and itself
2. 3 • 3 = 9
3. 3 is a prime number
1. A prime number is a number whose only factors are 1 and itself
2. 2, 2, 3, and 3 are prime factors because they are prime numbers and can be multiplied together to get 36
1. A prime number is a number whose only factors are 1 and itself
2. 6 • 9 = 54
3. Unfortunately, neither 6 nor 9 are prime
1. A prime number is a number whose only factors are 1 and itself
2. 2 • 3 = 6
3. 2 and 3 are prime numbers
1. A prime number is a number whose only factors are 1 and itself
2. 3 • 3 = 9
3. 3 is a prime number
1. A prime number is a number whose only factors are 1 and itself
2. 2, 3, 3, and 3 are prime factors because they are prime numbers and can be multiplied together to get 54
1. To find the greatest common factor, we need to multiply together all the shared factors
1. 2 is our first shared prime factor
1. The second 2 in 36 is not shared with 54
1. 3 is the second shared prime factor
1. 3 is the third shared prime factor
1. There are no other shared prime factors in from 36 and 54
1. Multiply together 2, 3, and 3
1. The three common factors are 2, 3, and 3
1. 2 • 3 • 3 = 18

Find the greatest common factor for 36 and 54