What is the Greatest Common Factor of 19865 and 19880?

Greatest common factor (GCF) of 19865 and 19880 is 5.

GCF(19865,19880) = 5

We will now calculate the prime factors of 19865 and 19880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19865 and 19880.

How to find the GCF of 19865 and 19880?

We will first find the prime factorization of 19865 and 19880. After we will calculate the factors of 19865 and 19880 and find the biggest common factor number .

Step-1: Prime Factorization of 19865

Prime factors of 19865 are 5, 29, 137. Prime factorization of 19865 in exponential form is:

19865 = 5¹ × 29¹ × 137¹

Step-2: Prime Factorization of 19880

Prime factors of 19880 are 2, 5, 7, 71. Prime factorization of 19880 in exponential form is:

19880 = 2³ × 5¹ × 7¹ × 71¹

Step-3: Factors of 19865

List of positive integer factors of 19865 that divides 19865 without a remainder.

1, 5, 29, 137, 145, 685, 3973

Step-4: Factors of 19880

List of positive integer factors of 19880 that divides 19865 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 71, 140, 142, 280, 284, 355, 497, 568, 710, 994, 1420, 1988, 2485, 2840, 3976, 4970, 9940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19865 and 19880. The biggest common factor number is the GCF number.
So the greatest common factor 19865 and 19880 is 5.

Also check out the Least Common Multiple of 19865 and 19880