What is the Greatest Common Factor of 52000 and 52020?

Greatest common factor (GCF) of 52000 and 52020 is 20.

GCF(52000,52020) = 20

We will now calculate the prime factors of 52000 and 52020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52020.

How to find the GCF of 52000 and 52020?

We will first find the prime factorization of 52000 and 52020. After we will calculate the factors of 52000 and 52020 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 52020

Prime factors of 52020 are 2, 3, 5, 17. Prime factorization of 52020 in exponential form is:

52020 = 2² × 3² × 5¹ × 17²

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 52020

List of positive integer factors of 52020 that divides 52000 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 30, 34, 36, 45, 51, 60, 68, 85, 90, 102, 153, 170, 180, 204, 255, 289, 306, 340, 510, 578, 612, 765, 867, 1020, 1156, 1445, 1530, 1734, 2601, 2890, 3060, 3468, 4335, 5202, 5780, 8670, 10404, 13005, 17340, 26010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52020. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52020 is 20.

Also check out the Least Common Multiple of 52000 and 52020