What is the Greatest Common Factor of 39208 and 39221?

Greatest common factor (GCF) of 39208 and 39221 is 13.

GCF(39208,39221) = 13

We will now calculate the prime factors of 39208 and 39221, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39208 and 39221.

How to find the GCF of 39208 and 39221?

We will first find the prime factorization of 39208 and 39221. After we will calculate the factors of 39208 and 39221 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 39221

Prime factors of 39221 are 7, 13, 431. Prime factorization of 39221 in exponential form is:

39221 = 7¹ × 13¹ × 431¹

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 39221

List of positive integer factors of 39221 that divides 39208 without a remainder.

1, 7, 13, 91, 431, 3017, 5603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39208 and 39221. The biggest common factor number is the GCF number.
So the greatest common factor 39208 and 39221 is 13.

Also check out the Least Common Multiple of 39208 and 39221