What is the Greatest Common Factor of 5264 and 5278?

Greatest common factor (GCF) of 5264 and 5278 is 14.

GCF(5264,5278) = 14

We will now calculate the prime factors of 5264 and 5278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5264 and 5278.

How to find the GCF of 5264 and 5278?

We will first find the prime factorization of 5264 and 5278. After we will calculate the factors of 5264 and 5278 and find the biggest common factor number .

Step-1: Prime Factorization of 5264

Prime factors of 5264 are 2, 7, 47. Prime factorization of 5264 in exponential form is:

5264 = 2⁴ × 7¹ × 47¹

Step-2: Prime Factorization of 5278

Prime factors of 5278 are 2, 7, 13, 29. Prime factorization of 5278 in exponential form is:

5278 = 2¹ × 7¹ × 13¹ × 29¹

Step-3: Factors of 5264

List of positive integer factors of 5264 that divides 5264 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 47, 56, 94, 112, 188, 329, 376, 658, 752, 1316, 2632

Step-4: Factors of 5278

List of positive integer factors of 5278 that divides 5264 without a remainder.

1, 2, 7, 13, 14, 26, 29, 58, 91, 182, 203, 377, 406, 754, 2639

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5264 and 5278. The biggest common factor number is the GCF number.
So the greatest common factor 5264 and 5278 is 14.

Also check out the Least Common Multiple of 5264 and 5278