What is the Greatest Common Factor of 35198 and 35214?

Greatest common factor (GCF) of 35198 and 35214 is 2.

GCF(35198,35214) = 2

We will now calculate the prime factors of 35198 and 35214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35198 and 35214.

How to find the GCF of 35198 and 35214?

We will first find the prime factorization of 35198 and 35214. After we will calculate the factors of 35198 and 35214 and find the biggest common factor number .

Step-1: Prime Factorization of 35198

Prime factors of 35198 are 2, 17599. Prime factorization of 35198 in exponential form is:

35198 = 2¹ × 17599¹

Step-2: Prime Factorization of 35214

Prime factors of 35214 are 2, 3, 5869. Prime factorization of 35214 in exponential form is:

35214 = 2¹ × 3¹ × 5869¹

Step-3: Factors of 35198

List of positive integer factors of 35198 that divides 35198 without a remainder.

1, 2, 17599

Step-4: Factors of 35214

List of positive integer factors of 35214 that divides 35198 without a remainder.

1, 2, 3, 6, 5869, 11738, 17607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35198 and 35214. The biggest common factor number is the GCF number.
So the greatest common factor 35198 and 35214 is 2.

Also check out the Least Common Multiple of 35198 and 35214