What is the Greatest Common Factor of 39299 and 39312?

Greatest common factor (GCF) of 39299 and 39312 is 13.

GCF(39299,39312) = 13

We will now calculate the prime factors of 39299 and 39312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39299 and 39312.

How to find the GCF of 39299 and 39312?

We will first find the prime factorization of 39299 and 39312. After we will calculate the factors of 39299 and 39312 and find the biggest common factor number .

Step-1: Prime Factorization of 39299

Prime factors of 39299 are 13, 3023. Prime factorization of 39299 in exponential form is:

39299 = 13¹ × 3023¹

Step-2: Prime Factorization of 39312

Prime factors of 39312 are 2, 3, 7, 13. Prime factorization of 39312 in exponential form is:

39312 = 2⁴ × 3³ × 7¹ × 13¹

Step-3: Factors of 39299

List of positive integer factors of 39299 that divides 39299 without a remainder.

1, 13, 3023

Step-4: Factors of 39312

List of positive integer factors of 39312 that divides 39299 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 27, 28, 36, 39, 42, 48, 52, 54, 56, 63, 72, 78, 84, 91, 104, 108, 112, 117, 126, 144, 156, 168, 182, 189, 208, 216, 234, 252, 273, 312, 336, 351, 364, 378, 432, 468, 504, 546, 624, 702, 728, 756, 819, 936, 1008, 1092, 1404, 1456, 1512, 1638, 1872, 2184, 2457, 2808, 3024, 3276, 4368, 4914, 5616, 6552, 9828, 13104, 19656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39299 and 39312. The biggest common factor number is the GCF number.
So the greatest common factor 39299 and 39312 is 13.

Also check out the Least Common Multiple of 39299 and 39312