What is the Greatest Common Factor of 25125 and 25140?

Greatest common factor (GCF) of 25125 and 25140 is 15.

GCF(25125,25140) = 15

We will now calculate the prime factors of 25125 and 25140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25125 and 25140.

How to find the GCF of 25125 and 25140?

We will first find the prime factorization of 25125 and 25140. After we will calculate the factors of 25125 and 25140 and find the biggest common factor number .

Step-1: Prime Factorization of 25125

Prime factors of 25125 are 3, 5, 67. Prime factorization of 25125 in exponential form is:

25125 = 3¹ × 5³ × 67¹

Step-2: Prime Factorization of 25140

Prime factors of 25140 are 2, 3, 5, 419. Prime factorization of 25140 in exponential form is:

25140 = 2² × 3¹ × 5¹ × 419¹

Step-3: Factors of 25125

List of positive integer factors of 25125 that divides 25125 without a remainder.

1, 3, 5, 15, 25, 67, 75, 125, 201, 335, 375, 1005, 1675, 5025, 8375

Step-4: Factors of 25140

List of positive integer factors of 25140 that divides 25125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 419, 838, 1257, 1676, 2095, 2514, 4190, 5028, 6285, 8380, 12570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25125 and 25140. The biggest common factor number is the GCF number.
So the greatest common factor 25125 and 25140 is 15.

Also check out the Least Common Multiple of 25125 and 25140