What is the Greatest Common Factor of 74496 and 74514?

Greatest common factor (GCF) of 74496 and 74514 is 6.

GCF(74496,74514) = 6

We will now calculate the prime factors of 74496 and 74514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74496 and 74514.

How to find the GCF of 74496 and 74514?

We will first find the prime factorization of 74496 and 74514. After we will calculate the factors of 74496 and 74514 and find the biggest common factor number .

Step-1: Prime Factorization of 74496

Prime factors of 74496 are 2, 3, 97. Prime factorization of 74496 in exponential form is:

74496 = 2⁸ × 3¹ × 97¹

Step-2: Prime Factorization of 74514

Prime factors of 74514 are 2, 3, 11, 1129. Prime factorization of 74514 in exponential form is:

74514 = 2¹ × 3¹ × 11¹ × 1129¹

Step-3: Factors of 74496

List of positive integer factors of 74496 that divides 74496 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 97, 128, 192, 194, 256, 291, 384, 388, 582, 768, 776, 1164, 1552, 2328, 3104, 4656, 6208, 9312, 12416, 18624, 24832, 37248

Step-4: Factors of 74514

List of positive integer factors of 74514 that divides 74496 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 1129, 2258, 3387, 6774, 12419, 24838, 37257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74496 and 74514. The biggest common factor number is the GCF number.
So the greatest common factor 74496 and 74514 is 6.

Also check out the Least Common Multiple of 74496 and 74514