What is the Greatest Common Factor of 39936 and 39952?

Greatest common factor (GCF) of 39936 and 39952 is 16.

GCF(39936,39952) = 16

We will now calculate the prime factors of 39936 and 39952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39936 and 39952.

How to find the GCF of 39936 and 39952?

We will first find the prime factorization of 39936 and 39952. After we will calculate the factors of 39936 and 39952 and find the biggest common factor number .

Step-1: Prime Factorization of 39936

Prime factors of 39936 are 2, 3, 13. Prime factorization of 39936 in exponential form is:

39936 = 2¹⁰ × 3¹ × 13¹

Step-2: Prime Factorization of 39952

Prime factors of 39952 are 2, 11, 227. Prime factorization of 39952 in exponential form is:

39952 = 2⁴ × 11¹ × 227¹

Step-3: Factors of 39936

List of positive integer factors of 39936 that divides 39936 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 512, 624, 768, 832, 1024, 1248, 1536, 1664, 2496, 3072, 3328, 4992, 6656, 9984, 13312, 19968

Step-4: Factors of 39952

List of positive integer factors of 39952 that divides 39936 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 227, 454, 908, 1816, 2497, 3632, 4994, 9988, 19976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39936 and 39952. The biggest common factor number is the GCF number.
So the greatest common factor 39936 and 39952 is 16.

Also check out the Least Common Multiple of 39936 and 39952