What is the Greatest Common Factor of 53985 and 54000?

Greatest common factor (GCF) of 53985 and 54000 is 15.

GCF(53985,54000) = 15

We will now calculate the prime factors of 53985 and 54000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53985 and 54000.

How to find the GCF of 53985 and 54000?

We will first find the prime factorization of 53985 and 54000. After we will calculate the factors of 53985 and 54000 and find the biggest common factor number .

Step-1: Prime Factorization of 53985

Prime factors of 53985 are 3, 5, 59, 61. Prime factorization of 53985 in exponential form is:

53985 = 3¹ × 5¹ × 59¹ × 61¹

Step-2: Prime Factorization of 54000

Prime factors of 54000 are 2, 3, 5. Prime factorization of 54000 in exponential form is:

54000 = 2⁴ × 3³ × 5³

Step-3: Factors of 53985

List of positive integer factors of 53985 that divides 53985 without a remainder.

1, 3, 5, 15, 59, 61, 177, 183, 295, 305, 885, 915, 3599, 10797, 17995

Step-4: Factors of 54000

List of positive integer factors of 54000 that divides 53985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 125, 135, 144, 150, 180, 200, 216, 225, 240, 250, 270, 300, 360, 375, 400, 432, 450, 500, 540, 600, 675, 720, 750, 900, 1000, 1080, 1125, 1200, 1350, 1500, 1800, 2000, 2160, 2250, 2700, 3000, 3375, 3600, 4500, 5400, 6000, 6750, 9000, 10800, 13500, 18000, 27000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53985 and 54000. The biggest common factor number is the GCF number.
So the greatest common factor 53985 and 54000 is 15.

Also check out the Least Common Multiple of 53985 and 54000