What is the Greatest Common Factor of 14200 and 14214?

Greatest common factor (GCF) of 14200 and 14214 is 2.

GCF(14200,14214) = 2

We will now calculate the prime factors of 14200 and 14214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14200 and 14214.

How to find the GCF of 14200 and 14214?

We will first find the prime factorization of 14200 and 14214. After we will calculate the factors of 14200 and 14214 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 14214

Prime factors of 14214 are 2, 3, 23, 103. Prime factorization of 14214 in exponential form is:

14214 = 2¹ × 3¹ × 23¹ × 103¹

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 14214

List of positive integer factors of 14214 that divides 14200 without a remainder.

1, 2, 3, 6, 23, 46, 69, 103, 138, 206, 309, 618, 2369, 4738, 7107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14200 and 14214. The biggest common factor number is the GCF number.
So the greatest common factor 14200 and 14214 is 2.

Also check out the Least Common Multiple of 14200 and 14214