What is the Greatest Common Factor of 10200 and 10217?

Greatest common factor (GCF) of 10200 and 10217 is 17.

GCF(10200,10217) = 17

We will now calculate the prime factors of 10200 and 10217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10200 and 10217.

How to find the GCF of 10200 and 10217?

We will first find the prime factorization of 10200 and 10217. After we will calculate the factors of 10200 and 10217 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 10217

Prime factors of 10217 are 17, 601. Prime factorization of 10217 in exponential form is:

10217 = 17¹ × 601¹

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 10217

List of positive integer factors of 10217 that divides 10200 without a remainder.

1, 17, 601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10200 and 10217. The biggest common factor number is the GCF number.
So the greatest common factor 10200 and 10217 is 17.

Also check out the Least Common Multiple of 10200 and 10217