What is the Greatest Common Factor of 82296 and 82314?

Greatest common factor (GCF) of 82296 and 82314 is 18.

GCF(82296,82314) = 18

We will now calculate the prime factors of 82296 and 82314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82296 and 82314.

How to find the GCF of 82296 and 82314?

We will first find the prime factorization of 82296 and 82314. After we will calculate the factors of 82296 and 82314 and find the biggest common factor number .

Step-1: Prime Factorization of 82296

Prime factors of 82296 are 2, 3, 127. Prime factorization of 82296 in exponential form is:

82296 = 2³ × 3⁴ × 127¹

Step-2: Prime Factorization of 82314

Prime factors of 82314 are 2, 3, 17, 269. Prime factorization of 82314 in exponential form is:

82314 = 2¹ × 3² × 17¹ × 269¹

Step-3: Factors of 82296

List of positive integer factors of 82296 that divides 82296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 127, 162, 216, 254, 324, 381, 508, 648, 762, 1016, 1143, 1524, 2286, 3048, 3429, 4572, 6858, 9144, 10287, 13716, 20574, 27432, 41148

Step-4: Factors of 82314

List of positive integer factors of 82314 that divides 82296 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 269, 306, 538, 807, 1614, 2421, 4573, 4842, 9146, 13719, 27438, 41157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82296 and 82314. The biggest common factor number is the GCF number.
So the greatest common factor 82296 and 82314 is 18.

Also check out the Least Common Multiple of 82296 and 82314