What is the Greatest Common Factor of 65000 and 65013?

Greatest common factor (GCF) of 65000 and 65013 is 13.

GCF(65000,65013) = 13

We will now calculate the prime factors of 65000 and 65013, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65000 and 65013.

How to find the GCF of 65000 and 65013?

We will first find the prime factorization of 65000 and 65013. After we will calculate the factors of 65000 and 65013 and find the biggest common factor number .

Step-1: Prime Factorization of 65000

Prime factors of 65000 are 2, 5, 13. Prime factorization of 65000 in exponential form is:

65000 = 2³ × 5⁴ × 13¹

Step-2: Prime Factorization of 65013

Prime factors of 65013 are 3, 13, 1667. Prime factorization of 65013 in exponential form is:

65013 = 3¹ × 13¹ × 1667¹

Step-3: Factors of 65000

List of positive integer factors of 65000 that divides 65000 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 625, 650, 1000, 1250, 1300, 1625, 2500, 2600, 3250, 5000, 6500, 8125, 13000, 16250, 32500

Step-4: Factors of 65013

List of positive integer factors of 65013 that divides 65000 without a remainder.

1, 3, 13, 39, 1667, 5001, 21671

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65000 and 65013. The biggest common factor number is the GCF number.
So the greatest common factor 65000 and 65013 is 13.

Also check out the Least Common Multiple of 65000 and 65013