What is the Greatest Common Factor of 65214 and 65234?

Greatest common factor (GCF) of 65214 and 65234 is 2.

GCF(65214,65234) = 2

We will now calculate the prime factors of 65214 and 65234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65214 and 65234.

How to find the GCF of 65214 and 65234?

We will first find the prime factorization of 65214 and 65234. After we will calculate the factors of 65214 and 65234 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65234

Prime factors of 65234 are 2, 13, 193. Prime factorization of 65234 in exponential form is:

65234 = 2¹ × 13² × 193¹

Step-3: Factors of 65214

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

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

Step-4: Factors of 65234

List of positive integer factors of 65234 that divides 65214 without a remainder.

1, 2, 13, 26, 169, 193, 338, 386, 2509, 5018, 32617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65214 and 65234. The biggest common factor number is the GCF number.
So the greatest common factor 65214 and 65234 is 2.

Also check out the Least Common Multiple of 65214 and 65234