What is the Greatest Common Factor of 14200 and 14210?

Greatest common factor (GCF) of 14200 and 14210 is 10.

GCF(14200,14210) = 10

We will now calculate the prime factors of 14200 and 14210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14200 and 14210.

How to find the GCF of 14200 and 14210?

We will first find the prime factorization of 14200 and 14210. After we will calculate the factors of 14200 and 14210 and find the biggest common factor number .

Step-1: Prime Factorization of 14200

Prime factors of 14200 are 2, 5, 71. Prime factorization of 14200 in exponential form is:

14200 = 2³ × 5² × 71¹

Step-2: Prime Factorization of 14210

Prime factors of 14210 are 2, 5, 7, 29. Prime factorization of 14210 in exponential form is:

14210 = 2¹ × 5¹ × 7² × 29¹

Step-3: Factors of 14200

List of positive integer factors of 14200 that divides 14200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 71, 100, 142, 200, 284, 355, 568, 710, 1420, 1775, 2840, 3550, 7100

Step-4: Factors of 14210

List of positive integer factors of 14210 that divides 14200 without a remainder.

1, 2, 5, 7, 10, 14, 29, 35, 49, 58, 70, 98, 145, 203, 245, 290, 406, 490, 1015, 1421, 2030, 2842, 7105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14200 and 14210. The biggest common factor number is the GCF number.
So the greatest common factor 14200 and 14210 is 10.

Also check out the Least Common Multiple of 14200 and 14210