What is the Greatest Common Factor of 19968 and 19980?

Greatest common factor (GCF) of 19968 and 19980 is 12.

GCF(19968,19980) = 12

We will now calculate the prime factors of 19968 and 19980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19968 and 19980.

How to find the GCF of 19968 and 19980?

We will first find the prime factorization of 19968 and 19980. After we will calculate the factors of 19968 and 19980 and find the biggest common factor number .

Step-1: Prime Factorization of 19968

Prime factors of 19968 are 2, 3, 13. Prime factorization of 19968 in exponential form is:

19968 = 2⁹ × 3¹ × 13¹

Step-2: 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-3: Factors of 19968

List of positive integer factors of 19968 that divides 19968 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 512, 624, 768, 832, 1248, 1536, 1664, 2496, 3328, 4992, 6656, 9984

Step-4: Factors of 19980

List of positive integer factors of 19980 that divides 19968 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19968 and 19980. The biggest common factor number is the GCF number.
So the greatest common factor 19968 and 19980 is 12.

Also check out the Least Common Multiple of 19968 and 19980