What is the Greatest Common Factor of 14205 and 14214?

Greatest common factor (GCF) of 14205 and 14214 is 3.

GCF(14205,14214) = 3

We will now calculate the prime factors of 14205 and 14214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14205 and 14214.

How to find the GCF of 14205 and 14214?

We will first find the prime factorization of 14205 and 14214. After we will calculate the factors of 14205 and 14214 and find the biggest common factor number .

Step-1: Prime Factorization of 14205

Prime factors of 14205 are 3, 5, 947. Prime factorization of 14205 in exponential form is:

14205 = 3¹ × 5¹ × 947¹

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 14205

List of positive integer factors of 14205 that divides 14205 without a remainder.

1, 3, 5, 15, 947, 2841, 4735

Step-4: Factors of 14214

List of positive integer factors of 14214 that divides 14205 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 14205 and 14214. The biggest common factor number is the GCF number.
So the greatest common factor 14205 and 14214 is 3.

Also check out the Least Common Multiple of 14205 and 14214