What is the Greatest Common Factor of 67065 and 67077?

Greatest common factor (GCF) of 67065 and 67077 is 3.

GCF(67065,67077) = 3

We will now calculate the prime factors of 67065 and 67077, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67065 and 67077.

How to find the GCF of 67065 and 67077?

We will first find the prime factorization of 67065 and 67077. After we will calculate the factors of 67065 and 67077 and find the biggest common factor number .

Step-1: Prime Factorization of 67065

Prime factors of 67065 are 3, 5, 17, 263. Prime factorization of 67065 in exponential form is:

67065 = 3¹ × 5¹ × 17¹ × 263¹

Step-2: Prime Factorization of 67077

Prime factors of 67077 are 3, 29, 257. Prime factorization of 67077 in exponential form is:

67077 = 3² × 29¹ × 257¹

Step-3: Factors of 67065

List of positive integer factors of 67065 that divides 67065 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 263, 789, 1315, 3945, 4471, 13413, 22355

Step-4: Factors of 67077

List of positive integer factors of 67077 that divides 67065 without a remainder.

1, 3, 9, 29, 87, 257, 261, 771, 2313, 7453, 22359

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67065 and 67077. The biggest common factor number is the GCF number.
So the greatest common factor 67065 and 67077 is 3.

Also check out the Least Common Multiple of 67065 and 67077