What is the Greatest Common Factor of 10200 and 10219?

Greatest common factor (GCF) of 10200 and 10219 is 1.

GCF(10200,10219) = 1

We will now calculate the prime factors of 10200 and 10219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10200 and 10219.

How to find the GCF of 10200 and 10219?

We will first find the prime factorization of 10200 and 10219. After we will calculate the factors of 10200 and 10219 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 10219

Prime factors of 10219 are 11, 929. Prime factorization of 10219 in exponential form is:

10219 = 11¹ × 929¹

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 10219

List of positive integer factors of 10219 that divides 10200 without a remainder.

1, 11, 929

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10200 and 10219. The biggest common factor number is the GCF number.
So the greatest common factor 10200 and 10219 is 1.

Also check out the Least Common Multiple of 10200 and 10219