What is the Greatest Common Factor of 10200 and 10209?

Greatest common factor (GCF) of 10200 and 10209 is 3.

GCF(10200,10209) = 3

We will now calculate the prime factors of 10200 and 10209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10200 and 10209.

How to find the GCF of 10200 and 10209?

We will first find the prime factorization of 10200 and 10209. After we will calculate the factors of 10200 and 10209 and find the biggest common factor number .

Step-1: Prime Factorization of 10200

Prime factors of 10200 are 2, 3, 5, 17. Prime factorization of 10200 in exponential form is:

10200 = 2³ × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 10209

Prime factors of 10209 are 3, 41, 83. Prime factorization of 10209 in exponential form is:

10209 = 3¹ × 41¹ × 83¹

Step-3: Factors of 10200

List of positive integer factors of 10200 that divides 10200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 25, 30, 34, 40, 50, 51, 60, 68, 75, 85, 100, 102, 120, 136, 150, 170, 200, 204, 255, 300, 340, 408, 425, 510, 600, 680, 850, 1020, 1275, 1700, 2040, 2550, 3400, 5100

Step-4: Factors of 10209

List of positive integer factors of 10209 that divides 10200 without a remainder.

1, 3, 41, 83, 123, 249, 3403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10200 and 10209. The biggest common factor number is the GCF number.
So the greatest common factor 10200 and 10209 is 3.

Also check out the Least Common Multiple of 10200 and 10209