What is the Greatest Common Factor of 13000 and 13020?

Greatest common factor (GCF) of 13000 and 13020 is 20.

GCF(13000,13020) = 20

We will now calculate the prime factors of 13000 and 13020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13000 and 13020.

How to find the GCF of 13000 and 13020?

We will first find the prime factorization of 13000 and 13020. After we will calculate the factors of 13000 and 13020 and find the biggest common factor number .

Step-1: Prime Factorization of 13000

Prime factors of 13000 are 2, 5, 13. Prime factorization of 13000 in exponential form is:

13000 = 2³ × 5³ × 13¹

Step-2: Prime Factorization of 13020

Prime factors of 13020 are 2, 3, 5, 7, 31. Prime factorization of 13020 in exponential form is:

13020 = 2² × 3¹ × 5¹ × 7¹ × 31¹

Step-3: Factors of 13000

List of positive integer factors of 13000 that divides 13000 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 650, 1000, 1300, 1625, 2600, 3250, 6500

Step-4: Factors of 13020

List of positive integer factors of 13020 that divides 13000 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 31, 35, 42, 60, 62, 70, 84, 93, 105, 124, 140, 155, 186, 210, 217, 310, 372, 420, 434, 465, 620, 651, 868, 930, 1085, 1302, 1860, 2170, 2604, 3255, 4340, 6510

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13000 and 13020. The biggest common factor number is the GCF number.
So the greatest common factor 13000 and 13020 is 20.

Also check out the Least Common Multiple of 13000 and 13020