What is the Greatest Common Factor of 36000 and 36006?

Greatest common factor (GCF) of 36000 and 36006 is 6.

GCF(36000,36006) = 6

We will now calculate the prime factors of 36000 and 36006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36000 and 36006.

How to find the GCF of 36000 and 36006?

We will first find the prime factorization of 36000 and 36006. After we will calculate the factors of 36000 and 36006 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 36006

Prime factors of 36006 are 2, 3, 17, 353. Prime factorization of 36006 in exponential form is:

36006 = 2¹ × 3¹ × 17¹ × 353¹

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 36006

List of positive integer factors of 36006 that divides 36000 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 353, 706, 1059, 2118, 6001, 12002, 18003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36000 and 36006. The biggest common factor number is the GCF number.
So the greatest common factor 36000 and 36006 is 6.

Also check out the Least Common Multiple of 36000 and 36006