What is the Greatest Common Factor of 1125 and 1140?

Greatest common factor (GCF) of 1125 and 1140 is 15.

GCF(1125,1140) = 15

We will now calculate the prime factors of 1125 and 1140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1125 and 1140.

How to find the GCF of 1125 and 1140?

We will first find the prime factorization of 1125 and 1140. After we will calculate the factors of 1125 and 1140 and find the biggest common factor number .

Step-1: Prime Factorization of 1125

Prime factors of 1125 are 3, 5. Prime factorization of 1125 in exponential form is:

1125 = 3² × 5³

Step-2: Prime Factorization of 1140

Prime factors of 1140 are 2, 3, 5, 19. Prime factorization of 1140 in exponential form is:

1140 = 2² × 3¹ × 5¹ × 19¹

Step-3: Factors of 1125

List of positive integer factors of 1125 that divides 1125 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375

Step-4: Factors of 1140

List of positive integer factors of 1140 that divides 1125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1125 and 1140. The biggest common factor number is the GCF number.
So the greatest common factor 1125 and 1140 is 15.

Also check out the Least Common Multiple of 1125 and 1140