What is the Greatest Common Factor of 73296 and 73314?

Greatest common factor (GCF) of 73296 and 73314 is 18.

GCF(73296,73314) = 18

We will now calculate the prime factors of 73296 and 73314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73296 and 73314.

How to find the GCF of 73296 and 73314?

We will first find the prime factorization of 73296 and 73314. After we will calculate the factors of 73296 and 73314 and find the biggest common factor number .

Step-1: Prime Factorization of 73296

Prime factors of 73296 are 2, 3, 509. Prime factorization of 73296 in exponential form is:

73296 = 2⁴ × 3² × 509¹

Step-2: Prime Factorization of 73314

Prime factors of 73314 are 2, 3, 4073. Prime factorization of 73314 in exponential form is:

73314 = 2¹ × 3² × 4073¹

Step-3: Factors of 73296

List of positive integer factors of 73296 that divides 73296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 509, 1018, 1527, 2036, 3054, 4072, 4581, 6108, 8144, 9162, 12216, 18324, 24432, 36648

Step-4: Factors of 73314

List of positive integer factors of 73314 that divides 73296 without a remainder.

1, 2, 3, 6, 9, 18, 4073, 8146, 12219, 24438, 36657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73296 and 73314. The biggest common factor number is the GCF number.
So the greatest common factor 73296 and 73314 is 18.

Also check out the Least Common Multiple of 73296 and 73314