What is the Greatest Common Factor of 39888 and 39904?

Greatest common factor (GCF) of 39888 and 39904 is 16.

GCF(39888,39904) = 16

We will now calculate the prime factors of 39888 and 39904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39888 and 39904.

How to find the GCF of 39888 and 39904?

We will first find the prime factorization of 39888 and 39904. After we will calculate the factors of 39888 and 39904 and find the biggest common factor number .

Step-1: Prime Factorization of 39888

Prime factors of 39888 are 2, 3, 277. Prime factorization of 39888 in exponential form is:

39888 = 2⁴ × 3² × 277¹

Step-2: 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-3: Factors of 39888

List of positive integer factors of 39888 that divides 39888 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277, 554, 831, 1108, 1662, 2216, 2493, 3324, 4432, 4986, 6648, 9972, 13296, 19944

Step-4: Factors of 39904

List of positive integer factors of 39904 that divides 39888 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39888 and 39904. The biggest common factor number is the GCF number.
So the greatest common factor 39888 and 39904 is 16.

Also check out the Least Common Multiple of 39888 and 39904