What is the Greatest Common Factor of 25984 and 26000?

Greatest common factor (GCF) of 25984 and 26000 is 16.

GCF(25984,26000) = 16

We will now calculate the prime factors of 25984 and 26000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25984 and 26000.

How to find the GCF of 25984 and 26000?

We will first find the prime factorization of 25984 and 26000. After we will calculate the factors of 25984 and 26000 and find the biggest common factor number .

Step-1: Prime Factorization of 25984

Prime factors of 25984 are 2, 7, 29. Prime factorization of 25984 in exponential form is:

25984 = 2⁷ × 7¹ × 29¹

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 25984

List of positive integer factors of 25984 that divides 25984 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 29, 32, 56, 58, 64, 112, 116, 128, 203, 224, 232, 406, 448, 464, 812, 896, 928, 1624, 1856, 3248, 3712, 6496, 12992

Step-4: Factors of 26000

List of positive integer factors of 26000 that divides 25984 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 25984 and 26000. The biggest common factor number is the GCF number.
So the greatest common factor 25984 and 26000 is 16.

Also check out the Least Common Multiple of 25984 and 26000