What is the Greatest Common Factor of 25198 and 25214?

Greatest common factor (GCF) of 25198 and 25214 is 2.

GCF(25198,25214) = 2

We will now calculate the prime factors of 25198 and 25214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25198 and 25214.

How to find the GCF of 25198 and 25214?

We will first find the prime factorization of 25198 and 25214. After we will calculate the factors of 25198 and 25214 and find the biggest common factor number .

Step-1: Prime Factorization of 25198

Prime factors of 25198 are 2, 43, 293. Prime factorization of 25198 in exponential form is:

25198 = 2¹ × 43¹ × 293¹

Step-2: Prime Factorization of 25214

Prime factors of 25214 are 2, 7, 1801. Prime factorization of 25214 in exponential form is:

25214 = 2¹ × 7¹ × 1801¹

Step-3: Factors of 25198

List of positive integer factors of 25198 that divides 25198 without a remainder.

1, 2, 43, 86, 293, 586, 12599

Step-4: Factors of 25214

List of positive integer factors of 25214 that divides 25198 without a remainder.

1, 2, 7, 14, 1801, 3602, 12607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25198 and 25214. The biggest common factor number is the GCF number.
So the greatest common factor 25198 and 25214 is 2.

Also check out the Least Common Multiple of 25198 and 25214