What is the Greatest Common Factor of 7208 and 7225?

Greatest common factor (GCF) of 7208 and 7225 is 17.

GCF(7208,7225) = 17

We will now calculate the prime factors of 7208 and 7225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7208 and 7225.

How to find the GCF of 7208 and 7225?

We will first find the prime factorization of 7208 and 7225. After we will calculate the factors of 7208 and 7225 and find the biggest common factor number .

Step-1: Prime Factorization of 7208

Prime factors of 7208 are 2, 17, 53. Prime factorization of 7208 in exponential form is:

7208 = 2³ × 17¹ × 53¹

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 7208

List of positive integer factors of 7208 that divides 7208 without a remainder.

1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604

Step-4: Factors of 7225

List of positive integer factors of 7225 that divides 7208 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 7208 and 7225. The biggest common factor number is the GCF number.
So the greatest common factor 7208 and 7225 is 17.

Also check out the Least Common Multiple of 7208 and 7225