What is the Greatest Common Factor of 19968 and 19987?

Greatest common factor (GCF) of 19968 and 19987 is 1.

GCF(19968,19987) = 1

We will now calculate the prime factors of 19968 and 19987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19968 and 19987.

How to find the GCF of 19968 and 19987?

We will first find the prime factorization of 19968 and 19987. After we will calculate the factors of 19968 and 19987 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 19987

Prime factors of 19987 are 11, 23, 79. Prime factorization of 19987 in exponential form is:

19987 = 11¹ × 23¹ × 79¹

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 19987

List of positive integer factors of 19987 that divides 19968 without a remainder.

1, 11, 23, 79, 253, 869, 1817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19968 and 19987. The biggest common factor number is the GCF number.
So the greatest common factor 19968 and 19987 is 1.

Also check out the Least Common Multiple of 19968 and 19987