What is the Greatest Common Factor of 7210 and 7224?

Greatest common factor (GCF) of 7210 and 7224 is 14.

GCF(7210,7224) = 14

We will now calculate the prime factors of 7210 and 7224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7210 and 7224.

How to find the GCF of 7210 and 7224?

We will first find the prime factorization of 7210 and 7224. After we will calculate the factors of 7210 and 7224 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 7224

Prime factors of 7224 are 2, 3, 7, 43. Prime factorization of 7224 in exponential form is:

7224 = 2³ × 3¹ × 7¹ × 43¹

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 7224

List of positive integer factors of 7224 that divides 7210 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 43, 56, 84, 86, 129, 168, 172, 258, 301, 344, 516, 602, 903, 1032, 1204, 1806, 2408, 3612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7210 and 7224. The biggest common factor number is the GCF number.
So the greatest common factor 7210 and 7224 is 14.

Also check out the Least Common Multiple of 7210 and 7224