What is the Greatest Common Factor of 65000 and 65006?

Greatest common factor (GCF) of 65000 and 65006 is 2.

GCF(65000,65006) = 2

We will now calculate the prime factors of 65000 and 65006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65000 and 65006.

How to find the GCF of 65000 and 65006?

We will first find the prime factorization of 65000 and 65006. After we will calculate the factors of 65000 and 65006 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 65006

Prime factors of 65006 are 2, 32503. Prime factorization of 65006 in exponential form is:

65006 = 2¹ × 32503¹

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 65006

List of positive integer factors of 65006 that divides 65000 without a remainder.

1, 2, 32503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65000 and 65006. The biggest common factor number is the GCF number.
So the greatest common factor 65000 and 65006 is 2.

Also check out the Least Common Multiple of 65000 and 65006