What is the Greatest Common Factor of 67320 and 67338?

Greatest common factor (GCF) of 67320 and 67338 is 18.

GCF(67320,67338) = 18

We will now calculate the prime factors of 67320 and 67338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67320 and 67338.

How to find the GCF of 67320 and 67338?

We will first find the prime factorization of 67320 and 67338. After we will calculate the factors of 67320 and 67338 and find the biggest common factor number .

Step-1: Prime Factorization of 67320

Prime factors of 67320 are 2, 3, 5, 11, 17. Prime factorization of 67320 in exponential form is:

67320 = 2³ × 3² × 5¹ × 11¹ × 17¹

Step-2: Prime Factorization of 67338

Prime factors of 67338 are 2, 3, 29, 43. Prime factorization of 67338 in exponential form is:

67338 = 2¹ × 3³ × 29¹ × 43¹

Step-3: Factors of 67320

List of positive integer factors of 67320 that divides 67320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 17, 18, 20, 22, 24, 30, 33, 34, 36, 40, 44, 45, 51, 55, 60, 66, 68, 72, 85, 88, 90, 99, 102, 110, 120, 132, 136, 153, 165, 170, 180, 187, 198, 204, 220, 255, 264, 306, 330, 340, 360, 374, 396, 408, 440, 495, 510, 561, 612, 660, 680, 748, 765, 792, 935, 990, 1020, 1122, 1224, 1320, 1496, 1530, 1683, 1870, 1980, 2040, 2244, 2805, 3060, 3366, 3740, 3960, 4488, 5610, 6120, 6732, 7480, 8415, 11220, 13464, 16830, 22440, 33660

Step-4: Factors of 67338

List of positive integer factors of 67338 that divides 67320 without a remainder.

1, 2, 3, 6, 9, 18, 27, 29, 43, 54, 58, 86, 87, 129, 174, 258, 261, 387, 522, 774, 783, 1161, 1247, 1566, 2322, 2494, 3741, 7482, 11223, 22446, 33669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67320 and 67338. The biggest common factor number is the GCF number.
So the greatest common factor 67320 and 67338 is 18.

Also check out the Least Common Multiple of 67320 and 67338