What is the Greatest Common Factor of 26980 and 27000?

Greatest common factor (GCF) of 26980 and 27000 is 20.

GCF(26980,27000) = 20

We will now calculate the prime factors of 26980 and 27000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26980 and 27000.

How to find the GCF of 26980 and 27000?

We will first find the prime factorization of 26980 and 27000. After we will calculate the factors of 26980 and 27000 and find the biggest common factor number .

Step-1: Prime Factorization of 26980

Prime factors of 26980 are 2, 5, 19, 71. Prime factorization of 26980 in exponential form is:

26980 = 2² × 5¹ × 19¹ × 71¹

Step-2: Prime Factorization of 27000

Prime factors of 27000 are 2, 3, 5. Prime factorization of 27000 in exponential form is:

27000 = 2³ × 3³ × 5³

Step-3: Factors of 26980

List of positive integer factors of 26980 that divides 26980 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 71, 76, 95, 142, 190, 284, 355, 380, 710, 1349, 1420, 2698, 5396, 6745, 13490

Step-4: Factors of 27000

List of positive integer factors of 27000 that divides 26980 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26980 and 27000. The biggest common factor number is the GCF number.
So the greatest common factor 26980 and 27000 is 20.

Also check out the Least Common Multiple of 26980 and 27000