What is the Greatest Common Factor of 27489 and 27500?

Greatest common factor (GCF) of 27489 and 27500 is 11.

GCF(27489,27500) = 11

We will now calculate the prime factors of 27489 and 27500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27489 and 27500.

How to find the GCF of 27489 and 27500?

We will first find the prime factorization of 27489 and 27500. After we will calculate the factors of 27489 and 27500 and find the biggest common factor number .

Step-1: Prime Factorization of 27489

Prime factors of 27489 are 3, 7, 11, 17. Prime factorization of 27489 in exponential form is:

27489 = 3¹ × 7² × 11¹ × 17¹

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 27489

List of positive integer factors of 27489 that divides 27489 without a remainder.

1, 3, 7, 11, 17, 21, 33, 49, 51, 77, 119, 147, 187, 231, 357, 539, 561, 833, 1309, 1617, 2499, 3927, 9163

Step-4: Factors of 27500

List of positive integer factors of 27500 that divides 27489 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 27489 and 27500. The biggest common factor number is the GCF number.
So the greatest common factor 27489 and 27500 is 11.

Also check out the Least Common Multiple of 27489 and 27500