What is the Greatest Common Factor of 67309 and 67320?

Greatest common factor (GCF) of 67309 and 67320 is 11.

GCF(67309,67320) = 11

We will now calculate the prime factors of 67309 and 67320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67309 and 67320.

How to find the GCF of 67309 and 67320?

We will first find the prime factorization of 67309 and 67320. After we will calculate the factors of 67309 and 67320 and find the biggest common factor number .

Step-1: Prime Factorization of 67309

Prime factors of 67309 are 11, 29, 211. Prime factorization of 67309 in exponential form is:

67309 = 11¹ × 29¹ × 211¹

Step-2: 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-3: Factors of 67309

List of positive integer factors of 67309 that divides 67309 without a remainder.

1, 11, 29, 211, 319, 2321, 6119

Step-4: Factors of 67320

List of positive integer factors of 67320 that divides 67309 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67309 and 67320. The biggest common factor number is the GCF number.
So the greatest common factor 67309 and 67320 is 11.

Also check out the Least Common Multiple of 67309 and 67320