What is the Greatest Common Factor of 5025 and 5040?

Greatest common factor (GCF) of 5025 and 5040 is 15.

GCF(5025,5040) = 15

We will now calculate the prime factors of 5025 and 5040, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5025 and 5040.

How to find the GCF of 5025 and 5040?

We will first find the prime factorization of 5025 and 5040. After we will calculate the factors of 5025 and 5040 and find the biggest common factor number .

Step-1: Prime Factorization of 5025

Prime factors of 5025 are 3, 5, 67. Prime factorization of 5025 in exponential form is:

5025 = 3¹ × 5² × 67¹

Step-2: Prime Factorization of 5040

Prime factors of 5040 are 2, 3, 5, 7. Prime factorization of 5040 in exponential form is:

5040 = 2⁴ × 3² × 5¹ × 7¹

Step-3: Factors of 5025

List of positive integer factors of 5025 that divides 5025 without a remainder.

1, 3, 5, 15, 25, 67, 75, 201, 335, 1005, 1675

Step-4: Factors of 5040

List of positive integer factors of 5040 that divides 5025 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5025 and 5040. The biggest common factor number is the GCF number.
So the greatest common factor 5025 and 5040 is 15.

Also check out the Least Common Multiple of 5025 and 5040