What is the Greatest Common Factor of 2005 and 2025?

Greatest common factor (GCF) of 2005 and 2025 is 5.

GCF(2005,2025) = 5

We will now calculate the prime factors of 2005 and 2025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2005 and 2025.

How to find the GCF of 2005 and 2025?

We will first find the prime factorization of 2005 and 2025. After we will calculate the factors of 2005 and 2025 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 2025

Prime factors of 2025 are 3, 5. Prime factorization of 2025 in exponential form is:

2025 = 3⁴ × 5²

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 2025

List of positive integer factors of 2025 that divides 2005 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2005 and 2025. The biggest common factor number is the GCF number.
So the greatest common factor 2005 and 2025 is 5.

Also check out the Least Common Multiple of 2005 and 2025