What is the Greatest Common Factor of 52000 and 52013?

Greatest common factor (GCF) of 52000 and 52013 is 13.

GCF(52000,52013) = 13

We will now calculate the prime factors of 52000 and 52013, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52013.

How to find the GCF of 52000 and 52013?

We will first find the prime factorization of 52000 and 52013. After we will calculate the factors of 52000 and 52013 and find the biggest common factor number .

Step-1: Prime Factorization of 52000

Prime factors of 52000 are 2, 5, 13. Prime factorization of 52000 in exponential form is:

52000 = 2⁵ × 5³ × 13¹

Step-2: Prime Factorization of 52013

Prime factors of 52013 are 13, 4001. Prime factorization of 52013 in exponential form is:

52013 = 13¹ × 4001¹

Step-3: Factors of 52000

List of positive integer factors of 52000 that divides 52000 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 125, 130, 160, 200, 208, 250, 260, 325, 400, 416, 500, 520, 650, 800, 1000, 1040, 1300, 1625, 2000, 2080, 2600, 3250, 4000, 5200, 6500, 10400, 13000, 26000

Step-4: Factors of 52013

List of positive integer factors of 52013 that divides 52000 without a remainder.

1, 13, 4001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52013. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52013 is 13.

Also check out the Least Common Multiple of 52000 and 52013