What is the Greatest Common Factor of 19980 and 19996?

Greatest common factor (GCF) of 19980 and 19996 is 4.

GCF(19980,19996) = 4

We will now calculate the prime factors of 19980 and 19996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19980 and 19996.

How to find the GCF of 19980 and 19996?

We will first find the prime factorization of 19980 and 19996. After we will calculate the factors of 19980 and 19996 and find the biggest common factor number .

Step-1: Prime Factorization of 19980

Prime factors of 19980 are 2, 3, 5, 37. Prime factorization of 19980 in exponential form is:

19980 = 2² × 3³ × 5¹ × 37¹

Step-2: Prime Factorization of 19996

Prime factors of 19996 are 2, 4999. Prime factorization of 19996 in exponential form is:

19996 = 2² × 4999¹

Step-3: Factors of 19980

List of positive integer factors of 19980 that divides 19980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37, 45, 54, 60, 74, 90, 108, 111, 135, 148, 180, 185, 222, 270, 333, 370, 444, 540, 555, 666, 740, 999, 1110, 1332, 1665, 1998, 2220, 3330, 3996, 4995, 6660, 9990

Step-4: Factors of 19996

List of positive integer factors of 19996 that divides 19980 without a remainder.

1, 2, 4, 4999, 9998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19980 and 19996. The biggest common factor number is the GCF number.
So the greatest common factor 19980 and 19996 is 4.

Also check out the Least Common Multiple of 19980 and 19996