What is the Greatest Common Factor of 67704 and 67717?

Greatest common factor (GCF) of 67704 and 67717 is 13.

GCF(67704,67717) = 13

We will now calculate the prime factors of 67704 and 67717, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67704 and 67717.

How to find the GCF of 67704 and 67717?

We will first find the prime factorization of 67704 and 67717. After we will calculate the factors of 67704 and 67717 and find the biggest common factor number .

Step-1: Prime Factorization of 67704

Prime factors of 67704 are 2, 3, 7, 13, 31. Prime factorization of 67704 in exponential form is:

67704 = 2³ × 3¹ × 7¹ × 13¹ × 31¹

Step-2: Prime Factorization of 67717

Prime factors of 67717 are 13, 5209. Prime factorization of 67717 in exponential form is:

67717 = 13¹ × 5209¹

Step-3: Factors of 67704

List of positive integer factors of 67704 that divides 67704 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 31, 39, 42, 52, 56, 62, 78, 84, 91, 93, 104, 124, 156, 168, 182, 186, 217, 248, 273, 312, 364, 372, 403, 434, 546, 651, 728, 744, 806, 868, 1092, 1209, 1302, 1612, 1736, 2184, 2418, 2604, 2821, 3224, 4836, 5208, 5642, 8463, 9672, 11284, 16926, 22568, 33852

Step-4: Factors of 67717

List of positive integer factors of 67717 that divides 67704 without a remainder.

1, 13, 5209

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67704 and 67717. The biggest common factor number is the GCF number.
So the greatest common factor 67704 and 67717 is 13.

Also check out the Least Common Multiple of 67704 and 67717