What is the Greatest Common Factor of 52000 and 52005?

Greatest common factor (GCF) of 52000 and 52005 is 5.

GCF(52000,52005) = 5

We will now calculate the prime factors of 52000 and 52005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52005.

How to find the GCF of 52000 and 52005?

We will first find the prime factorization of 52000 and 52005. After we will calculate the factors of 52000 and 52005 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 52005

Prime factors of 52005 are 3, 5, 3467. Prime factorization of 52005 in exponential form is:

52005 = 3¹ × 5¹ × 3467¹

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 52005

List of positive integer factors of 52005 that divides 52000 without a remainder.

1, 3, 5, 15, 3467, 10401, 17335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52005. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52005 is 5.

Also check out the Least Common Multiple of 52000 and 52005