What is the Greatest Common Factor of 74289 and 74304?

Greatest common factor (GCF) of 74289 and 74304 is 3.

GCF(74289,74304) = 3

We will now calculate the prime factors of 74289 and 74304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74289 and 74304.

How to find the GCF of 74289 and 74304?

We will first find the prime factorization of 74289 and 74304. After we will calculate the factors of 74289 and 74304 and find the biggest common factor number .

Step-1: Prime Factorization of 74289

Prime factors of 74289 are 3, 24763. Prime factorization of 74289 in exponential form is:

74289 = 3¹ × 24763¹

Step-2: 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-3: Factors of 74289

List of positive integer factors of 74289 that divides 74289 without a remainder.

1, 3, 24763

Step-4: Factors of 74304

List of positive integer factors of 74304 that divides 74289 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74289 and 74304. The biggest common factor number is the GCF number.
So the greatest common factor 74289 and 74304 is 3.

Also check out the Least Common Multiple of 74289 and 74304