What is the Greatest Common Factor of 10189 and 10200?

Greatest common factor (GCF) of 10189 and 10200 is 1.

GCF(10189,10200) = 1

We will now calculate the prime factors of 10189 and 10200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10189 and 10200.

How to find the GCF of 10189 and 10200?

We will first find the prime factorization of 10189 and 10200. After we will calculate the factors of 10189 and 10200 and find the biggest common factor number .

Step-1: Prime Factorization of 10189

Prime factors of 10189 are 23, 443. Prime factorization of 10189 in exponential form is:

10189 = 23¹ × 443¹

Step-2: 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-3: Factors of 10189

List of positive integer factors of 10189 that divides 10189 without a remainder.

1, 23, 443

Step-4: Factors of 10200

List of positive integer factors of 10200 that divides 10189 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10189 and 10200. The biggest common factor number is the GCF number.
So the greatest common factor 10189 and 10200 is 1.

Also check out the Least Common Multiple of 10189 and 10200