What is the Greatest Common Factor of 2005 and 2023?

Greatest common factor (GCF) of 2005 and 2023 is 1.

GCF(2005,2023) = 1

We will now calculate the prime factors of 2005 and 2023, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2005 and 2023.

How to find the GCF of 2005 and 2023?

We will first find the prime factorization of 2005 and 2023. After we will calculate the factors of 2005 and 2023 and find the biggest common factor number .

Step-1: Prime Factorization of 2005

Prime factors of 2005 are 5, 401. Prime factorization of 2005 in exponential form is:

2005 = 5¹ × 401¹

Step-2: Prime Factorization of 2023

Prime factors of 2023 are 7, 17. Prime factorization of 2023 in exponential form is:

2023 = 7¹ × 17²

Step-3: Factors of 2005

List of positive integer factors of 2005 that divides 2005 without a remainder.

1, 5, 401

Step-4: Factors of 2023

List of positive integer factors of 2023 that divides 2005 without a remainder.

1, 7, 17, 119, 289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2005 and 2023. The biggest common factor number is the GCF number.
So the greatest common factor 2005 and 2023 is 1.

Also check out the Least Common Multiple of 2005 and 2023