What is the Greatest Common Factor of 19964 and 19968?

Greatest common factor (GCF) of 19964 and 19968 is 4.

GCF(19964,19968) = 4

We will now calculate the prime factors of 19964 and 19968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19964 and 19968.

How to find the GCF of 19964 and 19968?

We will first find the prime factorization of 19964 and 19968. After we will calculate the factors of 19964 and 19968 and find the biggest common factor number .

Step-1: Prime Factorization of 19964

Prime factors of 19964 are 2, 7, 23, 31. Prime factorization of 19964 in exponential form is:

19964 = 2² × 7¹ × 23¹ × 31¹

Step-2: 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-3: Factors of 19964

List of positive integer factors of 19964 that divides 19964 without a remainder.

1, 2, 4, 7, 14, 23, 28, 31, 46, 62, 92, 124, 161, 217, 322, 434, 644, 713, 868, 1426, 2852, 4991, 9982

Step-4: Factors of 19968

List of positive integer factors of 19968 that divides 19964 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19964 and 19968. The biggest common factor number is the GCF number.
So the greatest common factor 19964 and 19968 is 4.

Also check out the Least Common Multiple of 19964 and 19968