How to Factor GCF

The GCF is determined by prime factorization.

The greatest common factor (GCF) of two (or more) positive integers is the largest positive integer that equally divides into the integers. It is also known as the greatest common divisor (GCD). The GCF of two numbers is found by using prime factorization and multiplying the factors common to both numbers. If the numbers are primes, however, they are not divisible by any number except themselves and one. The GCF is such cases is one.

Instructions

1. Find the prime factors of the first number. For example, to find the GCF of 100 and 12, find the prime factors of 100. The prime factors of 100 are 2 * 2 * 5 * 5.

2. Factor the second number into prime factors. The prime factors of 12 are 2 * 2 * 3.

3. Take the factors common to both numbers and multiply them to get the GCF. In this example, two 2s are common to both numbers. The GCF of 100 and 12, therefore, is 2 * 2, which equals 4.

4. Determine the prime factors and take the common prime factors to find the GCF of more than two numbers. The method is identical to finding the GCF of two numbers.

References

• Math Forum: LCM, GCF
• Math.com: The Greatest Common Factor
• Purplemath: LCM (Least Common Multiple) and GCF (Greatest Common Factor)