What is the Greatest Common Factor of 67305 and 67310?

Greatest common factor (GCF) of 67305 and 67310 is 5.

GCF(67305,67310) = 5

We will now calculate the prime factors of 67305 and 67310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67305 and 67310.

How to find the GCF of 67305 and 67310?

We will first find the prime factorization of 67305 and 67310. After we will calculate the factors of 67305 and 67310 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67310

Prime factors of 67310 are 2, 5, 53, 127. Prime factorization of 67310 in exponential form is:

67310 = 2¹ × 5¹ × 53¹ × 127¹

Step-3: Factors of 67305

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

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

Step-4: Factors of 67310

List of positive integer factors of 67310 that divides 67305 without a remainder.

1, 2, 5, 10, 53, 106, 127, 254, 265, 530, 635, 1270, 6731, 13462, 33655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67305 and 67310. The biggest common factor number is the GCF number.
So the greatest common factor 67305 and 67310 is 5.

Also check out the Least Common Multiple of 67305 and 67310