What is the Greatest Common Factor of 36000 and 36005?

Greatest common factor (GCF) of 36000 and 36005 is 5.

GCF(36000,36005) = 5

We will now calculate the prime factors of 36000 and 36005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36000 and 36005.

How to find the GCF of 36000 and 36005?

We will first find the prime factorization of 36000 and 36005. After we will calculate the factors of 36000 and 36005 and find the biggest common factor number .

Step-1: Prime Factorization of 36000

Prime factors of 36000 are 2, 3, 5. Prime factorization of 36000 in exponential form is:

36000 = 2⁵ × 3² × 5³

Step-2: Prime Factorization of 36005

Prime factors of 36005 are 5, 19, 379. Prime factorization of 36005 in exponential form is:

36005 = 5¹ × 19¹ × 379¹

Step-3: Factors of 36000

List of positive integer factors of 36000 that divides 36000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 200, 225, 240, 250, 288, 300, 360, 375, 400, 450, 480, 500, 600, 720, 750, 800, 900, 1000, 1125, 1200, 1440, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 4000, 4500, 6000, 7200, 9000, 12000, 18000

Step-4: Factors of 36005

List of positive integer factors of 36005 that divides 36000 without a remainder.

1, 5, 19, 95, 379, 1895, 7201

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36000 and 36005. The biggest common factor number is the GCF number.
So the greatest common factor 36000 and 36005 is 5.

Also check out the Least Common Multiple of 36000 and 36005