What is the Greatest Common Factor of 2067 and 2085?

Greatest common factor (GCF) of 2067 and 2085 is 3.

GCF(2067,2085) = 3

We will now calculate the prime factors of 2067 and 2085, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2067 and 2085.

How to find the GCF of 2067 and 2085?

We will first find the prime factorization of 2067 and 2085. After we will calculate the factors of 2067 and 2085 and find the biggest common factor number .

Step-1: Prime Factorization of 2067

Prime factors of 2067 are 3, 13, 53. Prime factorization of 2067 in exponential form is:

2067 = 3¹ × 13¹ × 53¹

Step-2: Prime Factorization of 2085

Prime factors of 2085 are 3, 5, 139. Prime factorization of 2085 in exponential form is:

2085 = 3¹ × 5¹ × 139¹

Step-3: Factors of 2067

List of positive integer factors of 2067 that divides 2067 without a remainder.

1, 3, 13, 39, 53, 159, 689

Step-4: Factors of 2085

List of positive integer factors of 2085 that divides 2067 without a remainder.

1, 3, 5, 15, 139, 417, 695

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2067 and 2085. The biggest common factor number is the GCF number.
So the greatest common factor 2067 and 2085 is 3.

Also check out the Least Common Multiple of 2067 and 2085