What is the Greatest Common Factor of 31089 and 31104?

Greatest common factor (GCF) of 31089 and 31104 is 3.

GCF(31089,31104) = 3

We will now calculate the prime factors of 31089 and 31104, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31089 and 31104.

How to find the GCF of 31089 and 31104?

We will first find the prime factorization of 31089 and 31104. After we will calculate the factors of 31089 and 31104 and find the biggest common factor number .

Step-1: Prime Factorization of 31089

Prime factors of 31089 are 3, 43, 241. Prime factorization of 31089 in exponential form is:

31089 = 3¹ × 43¹ × 241¹

Step-2: Prime Factorization of 31104

Prime factors of 31104 are 2, 3. Prime factorization of 31104 in exponential form is:

31104 = 2⁷ × 3⁵

Step-3: Factors of 31089

List of positive integer factors of 31089 that divides 31089 without a remainder.

1, 3, 43, 129, 241, 723, 10363

Step-4: Factors of 31104

List of positive integer factors of 31104 that divides 31089 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 288, 324, 384, 432, 486, 576, 648, 864, 972, 1152, 1296, 1728, 1944, 2592, 3456, 3888, 5184, 7776, 10368, 15552

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31089 and 31104. The biggest common factor number is the GCF number.
So the greatest common factor 31089 and 31104 is 3.

Also check out the Least Common Multiple of 31089 and 31104