What is the Greatest Common Factor of 1140 and 1148?

Greatest common factor (GCF) of 1140 and 1148 is 4.

GCF(1140,1148) = 4

We will now calculate the prime factors of 1140 and 1148, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1140 and 1148.

How to find the GCF of 1140 and 1148?

We will first find the prime factorization of 1140 and 1148. After we will calculate the factors of 1140 and 1148 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1148

Prime factors of 1148 are 2, 7, 41. Prime factorization of 1148 in exponential form is:

1148 = 2² × 7¹ × 41¹

Step-3: Factors of 1140

List of positive integer factors of 1140 that divides 1140 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

Step-4: Factors of 1148

List of positive integer factors of 1148 that divides 1140 without a remainder.

1, 2, 4, 7, 14, 28, 41, 82, 164, 287, 574

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1140 and 1148. The biggest common factor number is the GCF number.
So the greatest common factor 1140 and 1148 is 4.

Also check out the Least Common Multiple of 1140 and 1148