What is the Greatest Common Factor of 35985 and 36000?

Greatest common factor (GCF) of 35985 and 36000 is 15.

GCF(35985,36000) = 15

We will now calculate the prime factors of 35985 and 36000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35985 and 36000.

How to find the GCF of 35985 and 36000?

We will first find the prime factorization of 35985 and 36000. After we will calculate the factors of 35985 and 36000 and find the biggest common factor number .

Step-1: Prime Factorization of 35985

Prime factors of 35985 are 3, 5, 2399. Prime factorization of 35985 in exponential form is:

35985 = 3¹ × 5¹ × 2399¹

Step-2: 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-3: Factors of 35985

List of positive integer factors of 35985 that divides 35985 without a remainder.

1, 3, 5, 15, 2399, 7197, 11995

Step-4: Factors of 36000

List of positive integer factors of 36000 that divides 35985 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35985 and 36000. The biggest common factor number is the GCF number.
So the greatest common factor 35985 and 36000 is 15.

Also check out the Least Common Multiple of 35985 and 36000