What is the Greatest Common Factor of 1140 and 1160?

Greatest common factor (GCF) of 1140 and 1160 is 20.

GCF(1140,1160) = 20

We will now calculate the prime factors of 1140 and 1160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1140 and 1160.

How to find the GCF of 1140 and 1160?

We will first find the prime factorization of 1140 and 1160. After we will calculate the factors of 1140 and 1160 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 1160

Prime factors of 1160 are 2, 5, 29. Prime factorization of 1160 in exponential form is:

1160 = 2³ × 5¹ × 29¹

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 1160

List of positive integer factors of 1160 that divides 1140 without a remainder.

1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1140 and 1160. The biggest common factor number is the GCF number.
So the greatest common factor 1140 and 1160 is 20.

Also check out the Least Common Multiple of 1140 and 1160