What is the Greatest Common Factor of 2006 and 2025?

Greatest common factor (GCF) of 2006 and 2025 is 1.

GCF(2006,2025) = 1

We will now calculate the prime factors of 2006 and 2025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2006 and 2025.

How to find the GCF of 2006 and 2025?

We will first find the prime factorization of 2006 and 2025. After we will calculate the factors of 2006 and 2025 and find the biggest common factor number .

Step-1: Prime Factorization of 2006

Prime factors of 2006 are 2, 17, 59. Prime factorization of 2006 in exponential form is:

2006 = 2¹ × 17¹ × 59¹

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 2006

List of positive integer factors of 2006 that divides 2006 without a remainder.

1, 2, 17, 34, 59, 118, 1003

Step-4: Factors of 2025

List of positive integer factors of 2025 that divides 2006 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 2006 and 2025. The biggest common factor number is the GCF number.
So the greatest common factor 2006 and 2025 is 1.

Also check out the Least Common Multiple of 2006 and 2025