What is the Greatest Common Factor of 27480 and 27500?

Greatest common factor (GCF) of 27480 and 27500 is 20.

GCF(27480,27500) = 20

We will now calculate the prime factors of 27480 and 27500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27480 and 27500.

How to find the GCF of 27480 and 27500?

We will first find the prime factorization of 27480 and 27500. After we will calculate the factors of 27480 and 27500 and find the biggest common factor number .

Step-1: Prime Factorization of 27480

Prime factors of 27480 are 2, 3, 5, 229. Prime factorization of 27480 in exponential form is:

27480 = 2³ × 3¹ × 5¹ × 229¹

Step-2: Prime Factorization of 27500

Prime factors of 27500 are 2, 5, 11. Prime factorization of 27500 in exponential form is:

27500 = 2² × 5⁴ × 11¹

Step-3: Factors of 27480

List of positive integer factors of 27480 that divides 27480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 229, 458, 687, 916, 1145, 1374, 1832, 2290, 2748, 3435, 4580, 5496, 6870, 9160, 13740

Step-4: Factors of 27500

List of positive integer factors of 27500 that divides 27480 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 125, 220, 250, 275, 500, 550, 625, 1100, 1250, 1375, 2500, 2750, 5500, 6875, 13750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27480 and 27500. The biggest common factor number is the GCF number.
So the greatest common factor 27480 and 27500 is 20.

Also check out the Least Common Multiple of 27480 and 27500