What is the Greatest Common Factor of 67665 and 67678?

Greatest common factor (GCF) of 67665 and 67678 is 13.

GCF(67665,67678) = 13

We will now calculate the prime factors of 67665 and 67678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67665 and 67678.

How to find the GCF of 67665 and 67678?

We will first find the prime factorization of 67665 and 67678. After we will calculate the factors of 67665 and 67678 and find the biggest common factor number .

Step-1: Prime Factorization of 67665

Prime factors of 67665 are 3, 5, 13, 347. Prime factorization of 67665 in exponential form is:

67665 = 3¹ × 5¹ × 13¹ × 347¹

Step-2: Prime Factorization of 67678

Prime factors of 67678 are 2, 13, 19, 137. Prime factorization of 67678 in exponential form is:

67678 = 2¹ × 13¹ × 19¹ × 137¹

Step-3: Factors of 67665

List of positive integer factors of 67665 that divides 67665 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 347, 1041, 1735, 4511, 5205, 13533, 22555

Step-4: Factors of 67678

List of positive integer factors of 67678 that divides 67665 without a remainder.

1, 2, 13, 19, 26, 38, 137, 247, 274, 494, 1781, 2603, 3562, 5206, 33839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67665 and 67678. The biggest common factor number is the GCF number.
So the greatest common factor 67665 and 67678 is 13.

Also check out the Least Common Multiple of 67665 and 67678