What is the Greatest Common Factor of 67728 and 67746?

Greatest common factor (GCF) of 67728 and 67746 is 6.

GCF(67728,67746) = 6

We will now calculate the prime factors of 67728 and 67746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67728 and 67746.

How to find the GCF of 67728 and 67746?

We will first find the prime factorization of 67728 and 67746. After we will calculate the factors of 67728 and 67746 and find the biggest common factor number .

Step-1: Prime Factorization of 67728

Prime factors of 67728 are 2, 3, 17, 83. Prime factorization of 67728 in exponential form is:

67728 = 2⁴ × 3¹ × 17¹ × 83¹

Step-2: Prime Factorization of 67746

Prime factors of 67746 are 2, 3, 7, 1613. Prime factorization of 67746 in exponential form is:

67746 = 2¹ × 3¹ × 7¹ × 1613¹

Step-3: Factors of 67728

List of positive integer factors of 67728 that divides 67728 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 83, 102, 136, 166, 204, 249, 272, 332, 408, 498, 664, 816, 996, 1328, 1411, 1992, 2822, 3984, 4233, 5644, 8466, 11288, 16932, 22576, 33864

Step-4: Factors of 67746

List of positive integer factors of 67746 that divides 67728 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1613, 3226, 4839, 9678, 11291, 22582, 33873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67728 and 67746. The biggest common factor number is the GCF number.
So the greatest common factor 67728 and 67746 is 6.

Also check out the Least Common Multiple of 67728 and 67746