What is the Greatest Common Factor of 5300 and 5306?

Greatest common factor (GCF) of 5300 and 5306 is 2.

GCF(5300,5306) = 2

We will now calculate the prime factors of 5300 and 5306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5300 and 5306.

How to find the GCF of 5300 and 5306?

We will first find the prime factorization of 5300 and 5306. After we will calculate the factors of 5300 and 5306 and find the biggest common factor number .

Step-1: Prime Factorization of 5300

Prime factors of 5300 are 2, 5, 53. Prime factorization of 5300 in exponential form is:

5300 = 2² × 5² × 53¹

Step-2: Prime Factorization of 5306

Prime factors of 5306 are 2, 7, 379. Prime factorization of 5306 in exponential form is:

5306 = 2¹ × 7¹ × 379¹

Step-3: Factors of 5300

List of positive integer factors of 5300 that divides 5300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650

Step-4: Factors of 5306

List of positive integer factors of 5306 that divides 5300 without a remainder.

1, 2, 7, 14, 379, 758, 2653

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5300 and 5306. The biggest common factor number is the GCF number.
So the greatest common factor 5300 and 5306 is 2.

Also check out the Least Common Multiple of 5300 and 5306