What is the Greatest Common Factor of 2025 and 2040?

Greatest common factor (GCF) of 2025 and 2040 is 15.

GCF(2025,2040) = 15

We will now calculate the prime factors of 2025 and 2040, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2025 and 2040.

How to find the GCF of 2025 and 2040?

We will first find the prime factorization of 2025 and 2040. After we will calculate the factors of 2025 and 2040 and find the biggest common factor number .

Step-1: Prime Factorization of 2025

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

2025 = 3⁴ × 5²

Step-2: Prime Factorization of 2040

Prime factors of 2040 are 2, 3, 5, 17. Prime factorization of 2040 in exponential form is:

2040 = 2³ × 3¹ × 5¹ × 17¹

Step-3: Factors of 2025

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

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

Step-4: Factors of 2040

List of positive integer factors of 2040 that divides 2025 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2025 and 2040. The biggest common factor number is the GCF number.
So the greatest common factor 2025 and 2040 is 15.

Also check out the Least Common Multiple of 2025 and 2040