What is the Greatest Common Factor of 25987 and 26000?

Greatest common factor (GCF) of 25987 and 26000 is 13.

GCF(25987,26000) = 13

We will now calculate the prime factors of 25987 and 26000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25987 and 26000.

How to find the GCF of 25987 and 26000?

We will first find the prime factorization of 25987 and 26000. After we will calculate the factors of 25987 and 26000 and find the biggest common factor number .

Step-1: Prime Factorization of 25987

Prime factors of 25987 are 13, 1999. Prime factorization of 25987 in exponential form is:

25987 = 13¹ × 1999¹

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 25987

List of positive integer factors of 25987 that divides 25987 without a remainder.

1, 13, 1999

Step-4: Factors of 26000

List of positive integer factors of 26000 that divides 25987 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 25987 and 26000. The biggest common factor number is the GCF number.
So the greatest common factor 25987 and 26000 is 13.

Also check out the Least Common Multiple of 25987 and 26000