What is the Greatest Common Factor of 65200 and 65214?

Greatest common factor (GCF) of 65200 and 65214 is 2.

GCF(65200,65214) = 2

We will now calculate the prime factors of 65200 and 65214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65200 and 65214.

How to find the GCF of 65200 and 65214?

We will first find the prime factorization of 65200 and 65214. After we will calculate the factors of 65200 and 65214 and find the biggest common factor number .

Step-1: Prime Factorization of 65200

Prime factors of 65200 are 2, 5, 163. Prime factorization of 65200 in exponential form is:

65200 = 2⁴ × 5² × 163¹

Step-2: Prime Factorization of 65214

Prime factors of 65214 are 2, 3, 3623. Prime factorization of 65214 in exponential form is:

65214 = 2¹ × 3² × 3623¹

Step-3: Factors of 65200

List of positive integer factors of 65200 that divides 65200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 163, 200, 326, 400, 652, 815, 1304, 1630, 2608, 3260, 4075, 6520, 8150, 13040, 16300, 32600

Step-4: Factors of 65214

List of positive integer factors of 65214 that divides 65200 without a remainder.

1, 2, 3, 6, 9, 18, 3623, 7246, 10869, 21738, 32607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65200 and 65214. The biggest common factor number is the GCF number.
So the greatest common factor 65200 and 65214 is 2.

Also check out the Least Common Multiple of 65200 and 65214