What is the Greatest Common Factor of 10198 and 10208?

Greatest common factor (GCF) of 10198 and 10208 is 2.

GCF(10198,10208) = 2

We will now calculate the prime factors of 10198 and 10208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10198 and 10208.

How to find the GCF of 10198 and 10208?

We will first find the prime factorization of 10198 and 10208. After we will calculate the factors of 10198 and 10208 and find the biggest common factor number .

Step-1: Prime Factorization of 10198

Prime factors of 10198 are 2, 5099. Prime factorization of 10198 in exponential form is:

10198 = 2¹ × 5099¹

Step-2: Prime Factorization of 10208

Prime factors of 10208 are 2, 11, 29. Prime factorization of 10208 in exponential form is:

10208 = 2⁵ × 11¹ × 29¹

Step-3: Factors of 10198

List of positive integer factors of 10198 that divides 10198 without a remainder.

1, 2, 5099

Step-4: Factors of 10208

List of positive integer factors of 10208 that divides 10198 without a remainder.

1, 2, 4, 8, 11, 16, 22, 29, 32, 44, 58, 88, 116, 176, 232, 319, 352, 464, 638, 928, 1276, 2552, 5104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10198 and 10208. The biggest common factor number is the GCF number.
So the greatest common factor 10198 and 10208 is 2.

Also check out the Least Common Multiple of 10198 and 10208