What is the Greatest Common Factor of 10300 and 10310?

Greatest common factor (GCF) of 10300 and 10310 is 10.

GCF(10300,10310) = 10

We will now calculate the prime factors of 10300 and 10310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10300 and 10310.

How to find the GCF of 10300 and 10310?

We will first find the prime factorization of 10300 and 10310. After we will calculate the factors of 10300 and 10310 and find the biggest common factor number .

Step-1: Prime Factorization of 10300

Prime factors of 10300 are 2, 5, 103. Prime factorization of 10300 in exponential form is:

10300 = 2² × 5² × 103¹

Step-2: Prime Factorization of 10310

Prime factors of 10310 are 2, 5, 1031. Prime factorization of 10310 in exponential form is:

10310 = 2¹ × 5¹ × 1031¹

Step-3: Factors of 10300

List of positive integer factors of 10300 that divides 10300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 103, 206, 412, 515, 1030, 2060, 2575, 5150

Step-4: Factors of 10310

List of positive integer factors of 10310 that divides 10300 without a remainder.

1, 2, 5, 10, 1031, 2062, 5155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10300 and 10310. The biggest common factor number is the GCF number.
So the greatest common factor 10300 and 10310 is 10.

Also check out the Least Common Multiple of 10300 and 10310