What is the Greatest Common Factor of 1170 and 1185?

Greatest common factor (GCF) of 1170 and 1185 is 15.

GCF(1170,1185) = 15

We will now calculate the prime factors of 1170 and 1185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1170 and 1185.

How to find the GCF of 1170 and 1185?

We will first find the prime factorization of 1170 and 1185. After we will calculate the factors of 1170 and 1185 and find the biggest common factor number .

Step-1: Prime Factorization of 1170

Prime factors of 1170 are 2, 3, 5, 13. Prime factorization of 1170 in exponential form is:

1170 = 2¹ × 3² × 5¹ × 13¹

Step-2: Prime Factorization of 1185

Prime factors of 1185 are 3, 5, 79. Prime factorization of 1185 in exponential form is:

1185 = 3¹ × 5¹ × 79¹

Step-3: Factors of 1170

List of positive integer factors of 1170 that divides 1170 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585

Step-4: Factors of 1185

List of positive integer factors of 1185 that divides 1170 without a remainder.

1, 3, 5, 15, 79, 237, 395

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1170 and 1185. The biggest common factor number is the GCF number.
So the greatest common factor 1170 and 1185 is 15.

Also check out the Least Common Multiple of 1170 and 1185