What is the Greatest Common Factor of 2065 and 2074?

Greatest common factor (GCF) of 2065 and 2074 is 1.

GCF(2065,2074) = 1

We will now calculate the prime factors of 2065 and 2074, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2065 and 2074.

How to find the GCF of 2065 and 2074?

We will first find the prime factorization of 2065 and 2074. After we will calculate the factors of 2065 and 2074 and find the biggest common factor number .

Step-1: Prime Factorization of 2065

Prime factors of 2065 are 5, 7, 59. Prime factorization of 2065 in exponential form is:

2065 = 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 2074

Prime factors of 2074 are 2, 17, 61. Prime factorization of 2074 in exponential form is:

2074 = 2¹ × 17¹ × 61¹

Step-3: Factors of 2065

List of positive integer factors of 2065 that divides 2065 without a remainder.

1, 5, 7, 35, 59, 295, 413

Step-4: Factors of 2074

List of positive integer factors of 2074 that divides 2065 without a remainder.

1, 2, 17, 34, 61, 122, 1037

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2065 and 2074. The biggest common factor number is the GCF number.
So the greatest common factor 2065 and 2074 is 1.

Also check out the Least Common Multiple of 2065 and 2074