What is the Greatest Common Factor of 67724 and 67728?

Greatest common factor (GCF) of 67724 and 67728 is 4.

GCF(67724,67728) = 4

We will now calculate the prime factors of 67724 and 67728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67724 and 67728.

How to find the GCF of 67724 and 67728?

We will first find the prime factorization of 67724 and 67728. After we will calculate the factors of 67724 and 67728 and find the biggest common factor number .

Step-1: Prime Factorization of 67724

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

67724 = 2² × 16931¹

Step-2: 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-3: Factors of 67724

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

1, 2, 4, 16931, 33862

Step-4: Factors of 67728

List of positive integer factors of 67728 that divides 67724 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67724 and 67728. The biggest common factor number is the GCF number.
So the greatest common factor 67724 and 67728 is 4.

Also check out the Least Common Multiple of 67724 and 67728