What is the Greatest Common Factor of 74304 and 74320?

Greatest common factor (GCF) of 74304 and 74320 is 16.

GCF(74304,74320) = 16

We will now calculate the prime factors of 74304 and 74320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74304 and 74320.

How to find the GCF of 74304 and 74320?

We will first find the prime factorization of 74304 and 74320. After we will calculate the factors of 74304 and 74320 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 74320

Prime factors of 74320 are 2, 5, 929. Prime factorization of 74320 in exponential form is:

74320 = 2⁴ × 5¹ × 929¹

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 74320

List of positive integer factors of 74320 that divides 74304 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 929, 1858, 3716, 4645, 7432, 9290, 14864, 18580, 37160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74304 and 74320. The biggest common factor number is the GCF number.
So the greatest common factor 74304 and 74320 is 16.

Also check out the Least Common Multiple of 74304 and 74320