What is the Greatest Common Factor of 39208 and 39214?

Greatest common factor (GCF) of 39208 and 39214 is 2.

GCF(39208,39214) = 2

We will now calculate the prime factors of 39208 and 39214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39208 and 39214.

How to find the GCF of 39208 and 39214?

We will first find the prime factorization of 39208 and 39214. After we will calculate the factors of 39208 and 39214 and find the biggest common factor number .

Step-1: Prime Factorization of 39208

Prime factors of 39208 are 2, 13, 29. Prime factorization of 39208 in exponential form is:

39208 = 2³ × 13² × 29¹

Step-2: 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-3: Factors of 39208

List of positive integer factors of 39208 that divides 39208 without a remainder.

1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 169, 232, 338, 377, 676, 754, 1352, 1508, 3016, 4901, 9802, 19604

Step-4: Factors of 39214

List of positive integer factors of 39214 that divides 39208 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39208 and 39214. The biggest common factor number is the GCF number.
So the greatest common factor 39208 and 39214 is 2.

Also check out the Least Common Multiple of 39208 and 39214