What is the Greatest Common Factor of 39312 and 39319?

Greatest common factor (GCF) of 39312 and 39319 is 7.

GCF(39312,39319) = 7

We will now calculate the prime factors of 39312 and 39319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39312 and 39319.

How to find the GCF of 39312 and 39319?

We will first find the prime factorization of 39312 and 39319. After we will calculate the factors of 39312 and 39319 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39319

Prime factors of 39319 are 7, 41, 137. Prime factorization of 39319 in exponential form is:

39319 = 7¹ × 41¹ × 137¹

Step-3: Factors of 39312

List of positive integer factors of 39312 that divides 39312 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

Step-4: Factors of 39319

List of positive integer factors of 39319 that divides 39312 without a remainder.

1, 7, 41, 137, 287, 959, 5617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39312 and 39319. The biggest common factor number is the GCF number.
So the greatest common factor 39312 and 39319 is 7.

Also check out the Least Common Multiple of 39312 and 39319