What is the Greatest Common Factor of 19968 and 19984?

Greatest common factor (GCF) of 19968 and 19984 is 16.

GCF(19968,19984) = 16

We will now calculate the prime factors of 19968 and 19984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19968 and 19984.

How to find the GCF of 19968 and 19984?

We will first find the prime factorization of 19968 and 19984. After we will calculate the factors of 19968 and 19984 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 19984

Prime factors of 19984 are 2, 1249. Prime factorization of 19984 in exponential form is:

19984 = 2⁴ × 1249¹

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 19984

List of positive integer factors of 19984 that divides 19968 without a remainder.

1, 2, 4, 8, 16, 1249, 2498, 4996, 9992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19968 and 19984. The biggest common factor number is the GCF number.
So the greatest common factor 19968 and 19984 is 16.

Also check out the Least Common Multiple of 19968 and 19984