What is the Greatest Common Factor of 39214 and 39228?

Greatest common factor (GCF) of 39214 and 39228 is 14.

GCF(39214,39228) = 14

We will now calculate the prime factors of 39214 and 39228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39214 and 39228.

How to find the GCF of 39214 and 39228?

We will first find the prime factorization of 39214 and 39228. After we will calculate the factors of 39214 and 39228 and find the biggest common factor number .

Step-1: Prime Factorization of 39214

Prime factors of 39214 are 2, 7, 2801. Prime factorization of 39214 in exponential form is:

39214 = 2¹ × 7¹ × 2801¹

Step-2: Prime Factorization of 39228

Prime factors of 39228 are 2, 3, 7, 467. Prime factorization of 39228 in exponential form is:

39228 = 2² × 3¹ × 7¹ × 467¹

Step-3: Factors of 39214

List of positive integer factors of 39214 that divides 39214 without a remainder.

1, 2, 7, 14, 2801, 5602, 19607

Step-4: Factors of 39228

List of positive integer factors of 39228 that divides 39214 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 467, 934, 1401, 1868, 2802, 3269, 5604, 6538, 9807, 13076, 19614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39214 and 39228. The biggest common factor number is the GCF number.
So the greatest common factor 39214 and 39228 is 14.

Also check out the Least Common Multiple of 39214 and 39228