What is the Greatest Common Factor of 25980 and 26000?

Greatest common factor (GCF) of 25980 and 26000 is 20.

GCF(25980,26000) = 20

We will now calculate the prime factors of 25980 and 26000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25980 and 26000.

How to find the GCF of 25980 and 26000?

We will first find the prime factorization of 25980 and 26000. After we will calculate the factors of 25980 and 26000 and find the biggest common factor number .

Step-1: Prime Factorization of 25980

Prime factors of 25980 are 2, 3, 5, 433. Prime factorization of 25980 in exponential form is:

25980 = 2² × 3¹ × 5¹ × 433¹

Step-2: Prime Factorization of 26000

Prime factors of 26000 are 2, 5, 13. Prime factorization of 26000 in exponential form is:

26000 = 2⁴ × 5³ × 13¹

Step-3: Factors of 25980

List of positive integer factors of 25980 that divides 25980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 433, 866, 1299, 1732, 2165, 2598, 4330, 5196, 6495, 8660, 12990

Step-4: Factors of 26000

List of positive integer factors of 26000 that divides 25980 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 125, 130, 200, 208, 250, 260, 325, 400, 500, 520, 650, 1000, 1040, 1300, 1625, 2000, 2600, 3250, 5200, 6500, 13000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25980 and 26000. The biggest common factor number is the GCF number.
So the greatest common factor 25980 and 26000 is 20.

Also check out the Least Common Multiple of 25980 and 26000