What is the Greatest Common Factor of 26000 and 26009?

Greatest common factor (GCF) of 26000 and 26009 is 1.

GCF(26000,26009) = 1

We will now calculate the prime factors of 26000 and 26009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26000 and 26009.

How to find the GCF of 26000 and 26009?

We will first find the prime factorization of 26000 and 26009. After we will calculate the factors of 26000 and 26009 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 26009

Prime factors of 26009 are 31, 839. Prime factorization of 26009 in exponential form is:

26009 = 31¹ × 839¹

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 26009

List of positive integer factors of 26009 that divides 26000 without a remainder.

1, 31, 839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26000 and 26009. The biggest common factor number is the GCF number.
So the greatest common factor 26000 and 26009 is 1.

Also check out the Least Common Multiple of 26000 and 26009