What is the Greatest Common Factor of 7210 and 7214?

Greatest common factor (GCF) of 7210 and 7214 is 2.

GCF(7210,7214) = 2

We will now calculate the prime factors of 7210 and 7214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7210 and 7214.

How to find the GCF of 7210 and 7214?

We will first find the prime factorization of 7210 and 7214. After we will calculate the factors of 7210 and 7214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7214

Prime factors of 7214 are 2, 3607. Prime factorization of 7214 in exponential form is:

7214 = 2¹ × 3607¹

Step-3: Factors of 7210

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

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

Step-4: Factors of 7214

List of positive integer factors of 7214 that divides 7210 without a remainder.

1, 2, 3607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7210 and 7214. The biggest common factor number is the GCF number.
So the greatest common factor 7210 and 7214 is 2.

Also check out the Least Common Multiple of 7210 and 7214