Greatest Common Factor (GCF) | Elementary

The greatest common factor (GCF) is a factor which is shared by two or more numbers. Numbers can have more than one common factor, but the GCF designates the largest one.

To find the GCF using factors, I have to follow these steps:

1. I write the list of factors of each number.

2. I determine the common factors.

3. I identify the largest common factor.

What is the GCF of 16, 48, and 32?

1. I write the list of factors of each number.

2. I determine the common factors.

3. I identify the largest common factor.
   
   I notice that 16 is the greatest common divisor.

The GCF of 16, 48, and 32 is 16.

To find the GCF using prime factorization, I have to follow these steps:

1. I make a factor tree for each number. 

2. I write the prime factorization of each number.

3. I identify the prime factors shared by all the numbers.

4. I calculate the GCF by multiplying the common prime factors together.

What is the GCF of 16, 48, and 32?

I make a factor tree for each number.  Note: To learn how to make a factor tree for a number, I can read the concept sheet The Prime Factor Tree.
I write the prime factorization of each number. Note: To learn what a prime factor is, I can read the concept sheet Prime Factors and Prime Factorization.
I identify the prime factors shared by all the numbers. The common prime factors are 2, 2, 2, and 2.
I calculate the GCF by multiplying the common prime factors together.

The GCF of 16, 48, and 32 is 16.

To find the GCF using a table of common factors, I have to follow these steps:

1. I draw a table with the first column titled Common Factors. The labels of the other columns will correspond to the numbers whose GCF I need to find.

2. I check if there is a common factor between all the numbers. I enter the factor in the Common Factors column and the result of the division under each number.

3. I repeat the process until there is no common factor other than 1. 

4. I calculate the GCF by multiplying the common factors in the first column.

What is the GCF of 16, 48, and 32?

I draw a table with the first column titled Common Factors. The labels of the other columns will correspond to the numbers whose GCF I need to find.
I check if there is a common factor for all the numbers The numbers 16, 48, and 32 are all divisible by 2. I write the factor in the Common Factors column and the result of the division under each number.
I repeat the process until there is no common factor other than 1. The numbers 8, 24, and 16 are all divisible by 4. 8 ÷ 4 = 2 24 ÷ 4 = 6 16 ÷ 4 = 4 The numbers 2, 6, and 4 are all divisible by 2. 2 ÷ 2 = 1 6 ÷ 2 = 3 4 ÷ 2 = 2 The numbers 1, 3, and 2 can only all be divided by 1.
I calculate the GCF by multiplying the common factors in the first column.	2 x 4 x 2 = 16

The GCF of 16, 48, and 32 is 16.