What is the Greatest Common Factor of 31170 and 31185?

Greatest common factor (GCF) of 31170 and 31185 is 15.

GCF(31170,31185) = 15

We will now calculate the prime factors of 31170 and 31185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31170 and 31185.

How to find the GCF of 31170 and 31185?

We will first find the prime factorization of 31170 and 31185. After we will calculate the factors of 31170 and 31185 and find the biggest common factor number .

Step-1: Prime Factorization of 31170

Prime factors of 31170 are 2, 3, 5, 1039. Prime factorization of 31170 in exponential form is:

31170 = 2¹ × 3¹ × 5¹ × 1039¹

Step-2: Prime Factorization of 31185

Prime factors of 31185 are 3, 5, 7, 11. Prime factorization of 31185 in exponential form is:

31185 = 3⁴ × 5¹ × 7¹ × 11¹

Step-3: Factors of 31170

List of positive integer factors of 31170 that divides 31170 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1039, 2078, 3117, 5195, 6234, 10390, 15585

Step-4: Factors of 31185

List of positive integer factors of 31185 that divides 31170 without a remainder.

1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 35, 45, 55, 63, 77, 81, 99, 105, 135, 165, 189, 231, 297, 315, 385, 405, 495, 567, 693, 891, 945, 1155, 1485, 2079, 2835, 3465, 4455, 6237, 10395

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31170 and 31185. The biggest common factor number is the GCF number.
So the greatest common factor 31170 and 31185 is 15.

Also check out the Least Common Multiple of 31170 and 31185