What is the Greatest Common Factor of 67296 and 67305?

Greatest common factor (GCF) of 67296 and 67305 is 3.

GCF(67296,67305) = 3

We will now calculate the prime factors of 67296 and 67305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67296 and 67305.

How to find the GCF of 67296 and 67305?

We will first find the prime factorization of 67296 and 67305. After we will calculate the factors of 67296 and 67305 and find the biggest common factor number .

Step-1: Prime Factorization of 67296

Prime factors of 67296 are 2, 3, 701. Prime factorization of 67296 in exponential form is:

67296 = 2⁵ × 3¹ × 701¹

Step-2: Prime Factorization of 67305

Prime factors of 67305 are 3, 5, 7, 641. Prime factorization of 67305 in exponential form is:

67305 = 3¹ × 5¹ × 7¹ × 641¹

Step-3: Factors of 67296

List of positive integer factors of 67296 that divides 67296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 701, 1402, 2103, 2804, 4206, 5608, 8412, 11216, 16824, 22432, 33648

Step-4: Factors of 67305

List of positive integer factors of 67305 that divides 67296 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 641, 1923, 3205, 4487, 9615, 13461, 22435

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67296 and 67305. The biggest common factor number is the GCF number.
So the greatest common factor 67296 and 67305 is 3.

Also check out the Least Common Multiple of 67296 and 67305