Common Factors
Tap on 9, 12, 36, 60, 84, or 210 if they are factors of .
Tap on 9, 12, 36, 60, 84, or 210 if they are factors of .
The number 12 is a common factor of 180, 420, and 504 because its prime factorization can be found inside of the prime factorizations of 180, 420, and 504—it’s a factor of all three numbers.
The number 60 is a common factor of 180 and 420, but not of 504. The prime factorization of 60 can be found inside of the prime factorizations of 180 and 420, but not 504.
The number 84 is a common factor of 420 and 504, but not of 180. The prime factorization of 84 can be found inside of the prime factorizations of 420 and 504, but not 180.
Tap on the numbers that have () as a common factor:
Find all of the common factors of:
Use the keypad to enter the prime factorizations of each common factor.
The numbers 420 (2 × 2 × 3 × 5 × 7) and 504 (2 × 2 × 2 × 3 × 3 × 7) have twelve common factors:
Of the twelve common factors, the greatest common factor (GCF) of 420 and 504 is 84.
There are two methods we can use to find the greatest common factor. One method is to list all of the common factors and then choose the greatest one.
A second method is to keep adding prime factors to a prime factorization until we can’t add any more prime factors without going outside of the prime factorization of 420 or 504.
Use the keypad to add prime factors to the prime factorization of a common factor. Make sure the prime factorization fits inside of the prime factorizations of 420 and 504. The greatest common factor that we can find is 84.
Find the greatest common factor of and .
Use the keypad to add prime factors to the prime factorization of a common factor. When it is no longer possible to add any more prime factors, the common factor is the greatest common factor.