What is the Greatest Common Factor of 7225 and 7230?

Greatest common factor (GCF) of 7225 and 7230 is 5.

GCF(7225,7230) = 5

We will now calculate the prime factors of 7225 and 7230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7225 and 7230.

How to find the GCF of 7225 and 7230?

We will first find the prime factorization of 7225 and 7230. After we will calculate the factors of 7225 and 7230 and find the biggest common factor number .

Step-1: Prime Factorization of 7225

Prime factors of 7225 are 5, 17. Prime factorization of 7225 in exponential form is:

7225 = 5² × 17²

Step-2: Prime Factorization of 7230

Prime factors of 7230 are 2, 3, 5, 241. Prime factorization of 7230 in exponential form is:

7230 = 2¹ × 3¹ × 5¹ × 241¹

Step-3: Factors of 7225

List of positive integer factors of 7225 that divides 7225 without a remainder.

1, 5, 17, 25, 85, 289, 425, 1445

Step-4: Factors of 7230

List of positive integer factors of 7230 that divides 7225 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7225 and 7230. The biggest common factor number is the GCF number.
So the greatest common factor 7225 and 7230 is 5.

Also check out the Least Common Multiple of 7225 and 7230