What is the Greatest Common Factor of 39808 and 39824?

Greatest common factor (GCF) of 39808 and 39824 is 16.

GCF(39808,39824) = 16

We will now calculate the prime factors of 39808 and 39824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39808 and 39824.

How to find the GCF of 39808 and 39824?

We will first find the prime factorization of 39808 and 39824. After we will calculate the factors of 39808 and 39824 and find the biggest common factor number .

Step-1: Prime Factorization of 39808

Prime factors of 39808 are 2, 311. Prime factorization of 39808 in exponential form is:

39808 = 2⁷ × 311¹

Step-2: Prime Factorization of 39824

Prime factors of 39824 are 2, 19, 131. Prime factorization of 39824 in exponential form is:

39824 = 2⁴ × 19¹ × 131¹

Step-3: Factors of 39808

List of positive integer factors of 39808 that divides 39808 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 311, 622, 1244, 2488, 4976, 9952, 19904

Step-4: Factors of 39824

List of positive integer factors of 39824 that divides 39808 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 131, 152, 262, 304, 524, 1048, 2096, 2489, 4978, 9956, 19912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39808 and 39824. The biggest common factor number is the GCF number.
So the greatest common factor 39808 and 39824 is 16.

Also check out the Least Common Multiple of 39808 and 39824