What is the Greatest Common Factor of 39904 and 39920?

Greatest common factor (GCF) of 39904 and 39920 is 16.

GCF(39904,39920) = 16

We will now calculate the prime factors of 39904 and 39920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39904 and 39920.

How to find the GCF of 39904 and 39920?

We will first find the prime factorization of 39904 and 39920. After we will calculate the factors of 39904 and 39920 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 39920

Prime factors of 39920 are 2, 5, 499. Prime factorization of 39920 in exponential form is:

39920 = 2⁴ × 5¹ × 499¹

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 39920

List of positive integer factors of 39920 that divides 39904 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 499, 998, 1996, 2495, 3992, 4990, 7984, 9980, 19960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39904 and 39920. The biggest common factor number is the GCF number.
So the greatest common factor 39904 and 39920 is 16.

Also check out the Least Common Multiple of 39904 and 39920