What is the Greatest Common Factor of 39936 and 39949?

Greatest common factor (GCF) of 39936 and 39949 is 13.

GCF(39936,39949) = 13

We will now calculate the prime factors of 39936 and 39949, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39936 and 39949.

How to find the GCF of 39936 and 39949?

We will first find the prime factorization of 39936 and 39949. After we will calculate the factors of 39936 and 39949 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 39949

Prime factors of 39949 are 7, 13, 439. Prime factorization of 39949 in exponential form is:

39949 = 7¹ × 13¹ × 439¹

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 39949

List of positive integer factors of 39949 that divides 39936 without a remainder.

1, 7, 13, 91, 439, 3073, 5707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39936 and 39949. The biggest common factor number is the GCF number.
So the greatest common factor 39936 and 39949 is 13.

Also check out the Least Common Multiple of 39936 and 39949