What is the Greatest Common Factor of 82308 and 82320?

Greatest common factor (GCF) of 82308 and 82320 is 12.

GCF(82308,82320) = 12

We will now calculate the prime factors of 82308 and 82320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82308 and 82320.

How to find the GCF of 82308 and 82320?

We will first find the prime factorization of 82308 and 82320. After we will calculate the factors of 82308 and 82320 and find the biggest common factor number .

Step-1: Prime Factorization of 82308

Prime factors of 82308 are 2, 3, 19. Prime factorization of 82308 in exponential form is:

82308 = 2² × 3¹ × 19³

Step-2: Prime Factorization of 82320

Prime factors of 82320 are 2, 3, 5, 7. Prime factorization of 82320 in exponential form is:

82320 = 2⁴ × 3¹ × 5¹ × 7³

Step-3: Factors of 82308

List of positive integer factors of 82308 that divides 82308 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 361, 722, 1083, 1444, 2166, 4332, 6859, 13718, 20577, 27436, 41154

Step-4: Factors of 82320

List of positive integer factors of 82320 that divides 82308 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 98, 105, 112, 120, 140, 147, 168, 196, 210, 240, 245, 280, 294, 336, 343, 392, 420, 490, 560, 588, 686, 735, 784, 840, 980, 1029, 1176, 1372, 1470, 1680, 1715, 1960, 2058, 2352, 2744, 2940, 3430, 3920, 4116, 5145, 5488, 5880, 6860, 8232, 10290, 11760, 13720, 16464, 20580, 27440, 41160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82308 and 82320. The biggest common factor number is the GCF number.
So the greatest common factor 82308 and 82320 is 12.

Also check out the Least Common Multiple of 82308 and 82320