What is the Greatest Common Factor of 19880 and 19900?

Greatest common factor (GCF) of 19880 and 19900 is 20.

GCF(19880,19900) = 20

We will now calculate the prime factors of 19880 and 19900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19880 and 19900.

How to find the GCF of 19880 and 19900?

We will first find the prime factorization of 19880 and 19900. After we will calculate the factors of 19880 and 19900 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19900

Prime factors of 19900 are 2, 5, 199. Prime factorization of 19900 in exponential form is:

19900 = 2² × 5² × 199¹

Step-3: Factors of 19880

List of positive integer factors of 19880 that divides 19880 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

Step-4: Factors of 19900

List of positive integer factors of 19900 that divides 19880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 199, 398, 796, 995, 1990, 3980, 4975, 9950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19880 and 19900. The biggest common factor number is the GCF number.
So the greatest common factor 19880 and 19900 is 20.

Also check out the Least Common Multiple of 19880 and 19900