What is the Greatest Common Factor of 2261 and 2278?

Greatest common factor (GCF) of 2261 and 2278 is 17.

GCF(2261,2278) = 17

We will now calculate the prime factors of 2261 and 2278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2261 and 2278.

How to find the GCF of 2261 and 2278?

We will first find the prime factorization of 2261 and 2278. After we will calculate the factors of 2261 and 2278 and find the biggest common factor number .

Step-1: Prime Factorization of 2261

Prime factors of 2261 are 7, 17, 19. Prime factorization of 2261 in exponential form is:

2261 = 7¹ × 17¹ × 19¹

Step-2: Prime Factorization of 2278

Prime factors of 2278 are 2, 17, 67. Prime factorization of 2278 in exponential form is:

2278 = 2¹ × 17¹ × 67¹

Step-3: Factors of 2261

List of positive integer factors of 2261 that divides 2261 without a remainder.

1, 7, 17, 19, 119, 133, 323

Step-4: Factors of 2278

List of positive integer factors of 2278 that divides 2261 without a remainder.

1, 2, 17, 34, 67, 134, 1139

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2261 and 2278. The biggest common factor number is the GCF number.
So the greatest common factor 2261 and 2278 is 17.

Also check out the Least Common Multiple of 2261 and 2278