What is the Greatest Common Factor of 65000 and 65014?

Greatest common factor (GCF) of 65000 and 65014 is 2.

GCF(65000,65014) = 2

We will now calculate the prime factors of 65000 and 65014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65000 and 65014.

How to find the GCF of 65000 and 65014?

We will first find the prime factorization of 65000 and 65014. After we will calculate the factors of 65000 and 65014 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 65014

Prime factors of 65014 are 2, 32507. Prime factorization of 65014 in exponential form is:

65014 = 2¹ × 32507¹

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 65014

List of positive integer factors of 65014 that divides 65000 without a remainder.

1, 2, 32507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65000 and 65014. The biggest common factor number is the GCF number.
So the greatest common factor 65000 and 65014 is 2.

Also check out the Least Common Multiple of 65000 and 65014