www.VirtualNerd.com

How Do You Find the Greatest Common Factor of Three Numbers?

Find the greatest common factor of 126, 162 and 180

Summary

  1. GCF stands for 'greatest common factor'
  2. We need to find the prime factorization of each number
  3. The prime factorization of 126 is 2•3•3•7
  4. The prime factorization of 162 is 2•3•3•3•3
  5. The prime factorization of 180 is 2•2•3•3•5
  6. 2, 3, and 3 are common factors
  7. Multiply the common factors to get a GCF of 18

Notes

    1. We first need to write out the prime factorization of each number
    2. In other words, we need to break each number down to a multiplication of prime numbers
    3. Remember, a prime number is a number whose only factors are 1 and itself
    1. We need to find all the prime numbers that, when multiplied together, give us 126
    1. 2, 3, 3, and 7 are all prime, because their only factors are 1 and themselves
    2. If we multiply them together, they give us 126
    3. So this is the prime factorization of 126
    1. We need to find all the prime numbers that, when multiplied together, give us 162
    1. 2, 3, 3, 3, and 3 are all prime, because their only factors are 1 and themselves
    2. If we multiply them together, they give us 162
    3. So this is the prime factorization of 162
    1. We need to find all the prime numbers that, when multiplied together, give us 180
    1. 2, 2, 3, 3, and 5 are all prime, because their only factors are 1 and themselves
    2. If we multiply them together, they give us 180
    3. So this is the prime factorization of 180
    1. Now we need to see if our three numbers have any of the same factors
    1. Each of our three numbers has a factor of 2, so it is a common factor
    1. Each of our three numbers has a factor of 3, so it is a common factor
    1. In fact, each of our numbers has TWO factors of 3
    2. So we have TWO 3's as common factors
    1. Our common factors are the numbers we circled, 2, 3, and 3
    1. Our common factors are the numbers we circled, 2, 3, and 3
    1. To get the greatest common factor, we need to multiply the common factors
    2. Remember, our common factors were 2, 3, and 3
    1. Remember, our common factors were 2, 3, and 3
    1. 2•3•3=18
    2. So that makes 18 our greatest common factor!
    1. 2•3•3=18
    2. So that makes 18 our greatest common factor!