What is the Greatest Common Factor of 7259 and 7266?

Greatest common factor (GCF) of 7259 and 7266 is 7.

GCF(7259,7266) = 7

We will now calculate the prime factors of 7259 and 7266, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7259 and 7266.

How to find the GCF of 7259 and 7266?

We will first find the prime factorization of 7259 and 7266. After we will calculate the factors of 7259 and 7266 and find the biggest common factor number .

Step-1: Prime Factorization of 7259

Prime factors of 7259 are 7, 17, 61. Prime factorization of 7259 in exponential form is:

7259 = 7¹ × 17¹ × 61¹

Step-2: Prime Factorization of 7266

Prime factors of 7266 are 2, 3, 7, 173. Prime factorization of 7266 in exponential form is:

7266 = 2¹ × 3¹ × 7¹ × 173¹

Step-3: Factors of 7259

List of positive integer factors of 7259 that divides 7259 without a remainder.

1, 7, 17, 61, 119, 427, 1037

Step-4: Factors of 7266

List of positive integer factors of 7266 that divides 7259 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 173, 346, 519, 1038, 1211, 2422, 3633

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7259 and 7266. The biggest common factor number is the GCF number.
So the greatest common factor 7259 and 7266 is 7.

Also check out the Least Common Multiple of 7259 and 7266