What is the Greatest Common Factor of 39305 and 39312?

Greatest common factor (GCF) of 39305 and 39312 is 7.

GCF(39305,39312) = 7

We will now calculate the prime factors of 39305 and 39312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39305 and 39312.

How to find the GCF of 39305 and 39312?

We will first find the prime factorization of 39305 and 39312. After we will calculate the factors of 39305 and 39312 and find the biggest common factor number .

Step-1: Prime Factorization of 39305

Prime factors of 39305 are 5, 7, 1123. Prime factorization of 39305 in exponential form is:

39305 = 5¹ × 7¹ × 1123¹

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 39305

List of positive integer factors of 39305 that divides 39305 without a remainder.

1, 5, 7, 35, 1123, 5615, 7861

Step-4: Factors of 39312

List of positive integer factors of 39312 that divides 39305 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 39305 and 39312. The biggest common factor number is the GCF number.
So the greatest common factor 39305 and 39312 is 7.

Also check out the Least Common Multiple of 39305 and 39312