What is the Greatest Common Factor of 67728 and 67732?

Greatest common factor (GCF) of 67728 and 67732 is 4.

GCF(67728,67732) = 4

We will now calculate the prime factors of 67728 and 67732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67728 and 67732.

How to find the GCF of 67728 and 67732?

We will first find the prime factorization of 67728 and 67732. After we will calculate the factors of 67728 and 67732 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 67732

Prime factors of 67732 are 2, 7, 41, 59. Prime factorization of 67732 in exponential form is:

67732 = 2² × 7¹ × 41¹ × 59¹

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 67732

List of positive integer factors of 67732 that divides 67728 without a remainder.

1, 2, 4, 7, 14, 28, 41, 59, 82, 118, 164, 236, 287, 413, 574, 826, 1148, 1652, 2419, 4838, 9676, 16933, 33866

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67728 and 67732. The biggest common factor number is the GCF number.
So the greatest common factor 67728 and 67732 is 4.

Also check out the Least Common Multiple of 67728 and 67732