What is the Greatest Common Factor of 54000 and 54010?

Greatest common factor (GCF) of 54000 and 54010 is 10.

GCF(54000,54010) = 10

We will now calculate the prime factors of 54000 and 54010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54000 and 54010.

How to find the GCF of 54000 and 54010?

We will first find the prime factorization of 54000 and 54010. After we will calculate the factors of 54000 and 54010 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54010

Prime factors of 54010 are 2, 5, 11, 491. Prime factorization of 54010 in exponential form is:

54010 = 2¹ × 5¹ × 11¹ × 491¹

Step-3: Factors of 54000

List of positive integer factors of 54000 that divides 54000 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

Step-4: Factors of 54010

List of positive integer factors of 54010 that divides 54000 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 491, 982, 2455, 4910, 5401, 10802, 27005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54000 and 54010. The biggest common factor number is the GCF number.
So the greatest common factor 54000 and 54010 is 10.

Also check out the Least Common Multiple of 54000 and 54010