What is the Greatest Common Factor of 5300 and 5314?

Greatest common factor (GCF) of 5300 and 5314 is 2.

GCF(5300,5314) = 2

We will now calculate the prime factors of 5300 and 5314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5300 and 5314.

How to find the GCF of 5300 and 5314?

We will first find the prime factorization of 5300 and 5314. After we will calculate the factors of 5300 and 5314 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 5314

Prime factors of 5314 are 2, 2657. Prime factorization of 5314 in exponential form is:

5314 = 2¹ × 2657¹

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 5314

List of positive integer factors of 5314 that divides 5300 without a remainder.

1, 2, 2657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5300 and 5314. The biggest common factor number is the GCF number.
So the greatest common factor 5300 and 5314 is 2.

Also check out the Least Common Multiple of 5300 and 5314