What is the Greatest Common Factor of 26000 and 26014?

Greatest common factor (GCF) of 26000 and 26014 is 2.

GCF(26000,26014) = 2

We will now calculate the prime factors of 26000 and 26014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26000 and 26014.

How to find the GCF of 26000 and 26014?

We will first find the prime factorization of 26000 and 26014. After we will calculate the factors of 26000 and 26014 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 26014

Prime factors of 26014 are 2, 13007. Prime factorization of 26014 in exponential form is:

26014 = 2¹ × 13007¹

Step-3: Factors of 26000

List of positive integer factors of 26000 that divides 26000 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

Step-4: Factors of 26014

List of positive integer factors of 26014 that divides 26000 without a remainder.

1, 2, 13007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26000 and 26014. The biggest common factor number is the GCF number.
So the greatest common factor 26000 and 26014 is 2.

Also check out the Least Common Multiple of 26000 and 26014