What is the Greatest Common Factor of 7205 and 7225?

Greatest common factor (GCF) of 7205 and 7225 is 5.

GCF(7205,7225) = 5

We will now calculate the prime factors of 7205 and 7225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7205 and 7225.

How to find the GCF of 7205 and 7225?

We will first find the prime factorization of 7205 and 7225. After we will calculate the factors of 7205 and 7225 and find the biggest common factor number .

Step-1: Prime Factorization of 7205

Prime factors of 7205 are 5, 11, 131. Prime factorization of 7205 in exponential form is:

7205 = 5¹ × 11¹ × 131¹

Step-2: Prime Factorization of 7225

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

7225 = 5² × 17²

Step-3: Factors of 7205

List of positive integer factors of 7205 that divides 7205 without a remainder.

1, 5, 11, 55, 131, 655, 1441

Step-4: Factors of 7225

List of positive integer factors of 7225 that divides 7205 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7205 and 7225. The biggest common factor number is the GCF number.
So the greatest common factor 7205 and 7225 is 5.

Also check out the Least Common Multiple of 7205 and 7225