The greatest common factor (GCF) is the largest positive integer that divides evenly into two or more integers that are not all zero. It is also known as the greatest common divisor (GCD) or highest common factor (HCF) . The GCF is useful for simplifying fractions to their lowest terms.
There are different methods to find the GCF, including listing out the factors of each number and finding the common factors, and using prime factorization.
To find the GCF by listing out factors, you can:
- List out all the factors of each number.
- Identify the factors that are common to all the numbers.
- Choose the largest common factor as the GCF.
For example, to find the GCF of 12 and 30:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 3, 6
- Largest common factor: 6 Therefore, the GCF of 12 and 30 is 6.
To find the GCF by prime factorization, you can:
- Write each number as a product of its prime factors.
- Identify the common prime factors.
- Multiply the common prime factors to get the GCF.
For example, to find the GCF of 63 and 84:
- Prime factors of 63: 3 x 3 x 7
- Prime factors of 84: 2 x 2 x 3 x 7
- Common prime factors: 3 and 7
- Multiply common prime factors: 3 x 7 = 21 Therefore, the GCF of 63 and 84 is 21.
