What is the Greatest Common Factor of 19888 and 19900?

Greatest common factor (GCF) of 19888 and 19900 is 4.

GCF(19888,19900) = 4

We will now calculate the prime factors of 19888 and 19900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19888 and 19900.

How to find the GCF of 19888 and 19900?

We will first find the prime factorization of 19888 and 19900. After we will calculate the factors of 19888 and 19900 and find the biggest common factor number .

Step-1: Prime Factorization of 19888

Prime factors of 19888 are 2, 11, 113. Prime factorization of 19888 in exponential form is:

19888 = 2⁴ × 11¹ × 113¹

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 19888

List of positive integer factors of 19888 that divides 19888 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 113, 176, 226, 452, 904, 1243, 1808, 2486, 4972, 9944

Step-4: Factors of 19900

List of positive integer factors of 19900 that divides 19888 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 19888 and 19900. The biggest common factor number is the GCF number.
So the greatest common factor 19888 and 19900 is 4.

Also check out the Least Common Multiple of 19888 and 19900