What is the Greatest Common Factor of 10200 and 10214?

Greatest common factor (GCF) of 10200 and 10214 is 2.

GCF(10200,10214) = 2

We will now calculate the prime factors of 10200 and 10214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10200 and 10214.

How to find the GCF of 10200 and 10214?

We will first find the prime factorization of 10200 and 10214. After we will calculate the factors of 10200 and 10214 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 10214

Prime factors of 10214 are 2, 5107. Prime factorization of 10214 in exponential form is:

10214 = 2¹ × 5107¹

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 10214

List of positive integer factors of 10214 that divides 10200 without a remainder.

1, 2, 5107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10200 and 10214. The biggest common factor number is the GCF number.
So the greatest common factor 10200 and 10214 is 2.

Also check out the Least Common Multiple of 10200 and 10214