What is the Greatest Common Factor of 7196 and 7210?

Greatest common factor (GCF) of 7196 and 7210 is 14.

GCF(7196,7210) = 14

We will now calculate the prime factors of 7196 and 7210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7196 and 7210.

How to find the GCF of 7196 and 7210?

We will first find the prime factorization of 7196 and 7210. After we will calculate the factors of 7196 and 7210 and find the biggest common factor number .

Step-1: Prime Factorization of 7196

Prime factors of 7196 are 2, 7, 257. Prime factorization of 7196 in exponential form is:

7196 = 2² × 7¹ × 257¹

Step-2: Prime Factorization of 7210

Prime factors of 7210 are 2, 5, 7, 103. Prime factorization of 7210 in exponential form is:

7210 = 2¹ × 5¹ × 7¹ × 103¹

Step-3: Factors of 7196

List of positive integer factors of 7196 that divides 7196 without a remainder.

1, 2, 4, 7, 14, 28, 257, 514, 1028, 1799, 3598

Step-4: Factors of 7210

List of positive integer factors of 7210 that divides 7196 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 103, 206, 515, 721, 1030, 1442, 3605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7196 and 7210. The biggest common factor number is the GCF number.
So the greatest common factor 7196 and 7210 is 14.

Also check out the Least Common Multiple of 7196 and 7210