What is the Greatest Common Factor of 10198 and 10205?

Greatest common factor (GCF) of 10198 and 10205 is 1.

GCF(10198,10205) = 1

We will now calculate the prime factors of 10198 and 10205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10198 and 10205.

How to find the GCF of 10198 and 10205?

We will first find the prime factorization of 10198 and 10205. After we will calculate the factors of 10198 and 10205 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 10205

Prime factors of 10205 are 5, 13, 157. Prime factorization of 10205 in exponential form is:

10205 = 5¹ × 13¹ × 157¹

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 10205

List of positive integer factors of 10205 that divides 10198 without a remainder.

1, 5, 13, 65, 157, 785, 2041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10198 and 10205. The biggest common factor number is the GCF number.
So the greatest common factor 10198 and 10205 is 1.

Also check out the Least Common Multiple of 10198 and 10205