What is the Greatest Common Factor of 82302 and 82320?

Greatest common factor (GCF) of 82302 and 82320 is 6.

GCF(82302,82320) = 6

We will now calculate the prime factors of 82302 and 82320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82302 and 82320.

How to find the GCF of 82302 and 82320?

We will first find the prime factorization of 82302 and 82320. After we will calculate the factors of 82302 and 82320 and find the biggest common factor number .

Step-1: Prime Factorization of 82302

Prime factors of 82302 are 2, 3, 11, 29, 43. Prime factorization of 82302 in exponential form is:

82302 = 2¹ × 3¹ × 11¹ × 29¹ × 43¹

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 82302

List of positive integer factors of 82302 that divides 82302 without a remainder.

1, 2, 3, 6, 11, 22, 29, 33, 43, 58, 66, 86, 87, 129, 174, 258, 319, 473, 638, 946, 957, 1247, 1419, 1914, 2494, 2838, 3741, 7482, 13717, 27434, 41151

Step-4: Factors of 82320

List of positive integer factors of 82320 that divides 82302 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 82302 and 82320. The biggest common factor number is the GCF number.
So the greatest common factor 82302 and 82320 is 6.

Also check out the Least Common Multiple of 82302 and 82320