What is the Greatest Common Factor of 5300 and 5310?

Greatest common factor (GCF) of 5300 and 5310 is 10.

GCF(5300,5310) = 10

We will now calculate the prime factors of 5300 and 5310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5300 and 5310.

How to find the GCF of 5300 and 5310?

We will first find the prime factorization of 5300 and 5310. After we will calculate the factors of 5300 and 5310 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 5310

Prime factors of 5310 are 2, 3, 5, 59. Prime factorization of 5310 in exponential form is:

5310 = 2¹ × 3² × 5¹ × 59¹

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 5310

List of positive integer factors of 5310 that divides 5300 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 59, 90, 118, 177, 295, 354, 531, 590, 885, 1062, 1770, 2655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5300 and 5310. The biggest common factor number is the GCF number.
So the greatest common factor 5300 and 5310 is 10.

Also check out the Least Common Multiple of 5300 and 5310