What is the Greatest Common Factor of 74304 and 74319?

Greatest common factor (GCF) of 74304 and 74319 is 3.

GCF(74304,74319) = 3

We will now calculate the prime factors of 74304 and 74319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74304 and 74319.

How to find the GCF of 74304 and 74319?

We will first find the prime factorization of 74304 and 74319. After we will calculate the factors of 74304 and 74319 and find the biggest common factor number .

Step-1: Prime Factorization of 74304

Prime factors of 74304 are 2, 3, 43. Prime factorization of 74304 in exponential form is:

74304 = 2⁶ × 3³ × 43¹

Step-2: Prime Factorization of 74319

Prime factors of 74319 are 3, 7, 3539. Prime factorization of 74319 in exponential form is:

74319 = 3¹ × 7¹ × 3539¹

Step-3: Factors of 74304

List of positive integer factors of 74304 that divides 74304 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 43, 48, 54, 64, 72, 86, 96, 108, 129, 144, 172, 192, 216, 258, 288, 344, 387, 432, 516, 576, 688, 774, 864, 1032, 1161, 1376, 1548, 1728, 2064, 2322, 2752, 3096, 4128, 4644, 6192, 8256, 9288, 12384, 18576, 24768, 37152

Step-4: Factors of 74319

List of positive integer factors of 74319 that divides 74304 without a remainder.

1, 3, 7, 21, 3539, 10617, 24773

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74304 and 74319. The biggest common factor number is the GCF number.
So the greatest common factor 74304 and 74319 is 3.

Also check out the Least Common Multiple of 74304 and 74319