What is the Greatest Common Factor of 39904 and 39919?

Greatest common factor (GCF) of 39904 and 39919 is 1.

GCF(39904,39919) = 1

We will now calculate the prime factors of 39904 and 39919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39904 and 39919.

How to find the GCF of 39904 and 39919?

We will first find the prime factorization of 39904 and 39919. After we will calculate the factors of 39904 and 39919 and find the biggest common factor number .

Step-1: Prime Factorization of 39904

Prime factors of 39904 are 2, 29, 43. Prime factorization of 39904 in exponential form is:

39904 = 2⁵ × 29¹ × 43¹

Step-2: Prime Factorization of 39919

Prime factors of 39919 are 11, 19, 191. Prime factorization of 39919 in exponential form is:

39919 = 11¹ × 19¹ × 191¹

Step-3: Factors of 39904

List of positive integer factors of 39904 that divides 39904 without a remainder.

1, 2, 4, 8, 16, 29, 32, 43, 58, 86, 116, 172, 232, 344, 464, 688, 928, 1247, 1376, 2494, 4988, 9976, 19952

Step-4: Factors of 39919

List of positive integer factors of 39919 that divides 39904 without a remainder.

1, 11, 19, 191, 209, 2101, 3629

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39904 and 39919. The biggest common factor number is the GCF number.
So the greatest common factor 39904 and 39919 is 1.

Also check out the Least Common Multiple of 39904 and 39919