What is the Greatest Common Factor of 4125 and 4140?

Greatest common factor (GCF) of 4125 and 4140 is 15.

GCF(4125,4140) = 15

We will now calculate the prime factors of 4125 and 4140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4125 and 4140.

How to find the GCF of 4125 and 4140?

We will first find the prime factorization of 4125 and 4140. After we will calculate the factors of 4125 and 4140 and find the biggest common factor number .

Step-1: Prime Factorization of 4125

Prime factors of 4125 are 3, 5, 11. Prime factorization of 4125 in exponential form is:

4125 = 3¹ × 5³ × 11¹

Step-2: Prime Factorization of 4140

Prime factors of 4140 are 2, 3, 5, 23. Prime factorization of 4140 in exponential form is:

4140 = 2² × 3² × 5¹ × 23¹

Step-3: Factors of 4125

List of positive integer factors of 4125 that divides 4125 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 125, 165, 275, 375, 825, 1375

Step-4: Factors of 4140

List of positive integer factors of 4140 that divides 4125 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4125 and 4140. The biggest common factor number is the GCF number.
So the greatest common factor 4125 and 4140 is 15.

Also check out the Least Common Multiple of 4125 and 4140