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In this section, we learn how to find the GCF (Greatest Common Factor) for a group of numbers. The GCF is also known as the GCD (Greatest Common Divisor). This is a common source of confusion. If someone asks you to find the GCF or GCD for a group of numbers, they are asking for the same thing. The GCF is the largest whole number that each number in a group is divisible by. This means we could take each number in the group and divide by the GCF and there would be no remainder. How do we find the GCF?
Greatest Common Factor:
  1. Find the prime factorization of each number
  2. Create a list of prime factors that are common to all numbers
  3. The GCD is the product of the numbers on the list
Example 1: Find the GCF of 20 and 50
• 20 = 2 x 2 x 5
• 50 = 2 x 5 x 5
• Common: 2, 5
• Multiply: 2 x 5 = 10
GCF of 20 and 50 is 10
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