What is the Greatest Common Factor of 65000 and 65005?

Greatest common factor (GCF) of 65000 and 65005 is 5.

GCF(65000,65005) = 5

We will now calculate the prime factors of 65000 and 65005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65000 and 65005.

How to find the GCF of 65000 and 65005?

We will first find the prime factorization of 65000 and 65005. After we will calculate the factors of 65000 and 65005 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 65005

Prime factors of 65005 are 5, 13001. Prime factorization of 65005 in exponential form is:

65005 = 5¹ × 13001¹

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 65005

List of positive integer factors of 65005 that divides 65000 without a remainder.

1, 5, 13001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65000 and 65005. The biggest common factor number is the GCF number.
So the greatest common factor 65000 and 65005 is 5.

Also check out the Least Common Multiple of 65000 and 65005