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Greatest common factor
The greatest common factor (GCF), sometimes also referred to as the highest common factor (HCF) or the greatest common divisor (GCD), is the largest positive integer that a set of integers can all be divided by. For example, the largest number that 12, 24, and 32 can all be divided by is 4, so their greatest common factor is 4. Similarly, the largest number that 3, 5, and 10 can all be divided by is 1, so their greatest common factor is 1.
There are two ways to find the greatest common factor: listing the factors of each number and prime factorization.
Method 1: Listing the factors of each number
List all of the factors of each number and identify the largest (greatest) factor that all the numbers have in common.
12 - 1, 2, 3, 4, 6, 12
24 - 1, 2, 3, 4, 6, 8, 12, 24
32 - 1, 2, 3, 4, 8, 16, 32
4 is the greatest factor the numbers have in common, so it is the greatest common factor.
Method 2: Prime factorization
Use a factor tree to identify the prime factors (factors that are prime numbers) of each number. Identify the prime factors that all the numbers have in common and multiply them together to get the greatest common factor.
The prime factors that all of the numbers have in common are 2 and 2. Multiply these together to get the greatest common factor, 4.
There are two ways to find the greatest common factor: listing the factors of each number and prime factorization.
Method 1: Listing the factors of each number
List all of the factors of each number and identify the largest (greatest) factor that all the numbers have in common.
12 - 1, 2, 3, 4, 6, 12
24 - 1, 2, 3, 4, 6, 8, 12, 24
32 - 1, 2, 3, 4, 8, 16, 32
4 is the greatest factor the numbers have in common, so it is the greatest common factor.
Method 2: Prime factorization
Use a factor tree to identify the prime factors (factors that are prime numbers) of each number. Identify the prime factors that all the numbers have in common and multiply them together to get the greatest common factor.
The prime factors that all of the numbers have in common are 2 and 2. Multiply these together to get the greatest common factor, 4.