What is the Greatest Common Factor of 67704 and 67724?

Greatest common factor (GCF) of 67704 and 67724 is 4.

GCF(67704,67724) = 4

We will now calculate the prime factors of 67704 and 67724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67704 and 67724.

How to find the GCF of 67704 and 67724?

We will first find the prime factorization of 67704 and 67724. After we will calculate the factors of 67704 and 67724 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 67724

Prime factors of 67724 are 2, 16931. Prime factorization of 67724 in exponential form is:

67724 = 2² × 16931¹

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 67724

List of positive integer factors of 67724 that divides 67704 without a remainder.

1, 2, 4, 16931, 33862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67704 and 67724. The biggest common factor number is the GCF number.
So the greatest common factor 67704 and 67724 is 4.

Also check out the Least Common Multiple of 67704 and 67724