What is the Greatest Common Factor of 31140 and 31149?

Greatest common factor (GCF) of 31140 and 31149 is 9.

GCF(31140,31149) = 9

We will now calculate the prime factors of 31140 and 31149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31140 and 31149.

How to find the GCF of 31140 and 31149?

We will first find the prime factorization of 31140 and 31149. After we will calculate the factors of 31140 and 31149 and find the biggest common factor number .

Step-1: Prime Factorization of 31140

Prime factors of 31140 are 2, 3, 5, 173. Prime factorization of 31140 in exponential form is:

31140 = 2² × 3² × 5¹ × 173¹

Step-2: Prime Factorization of 31149

Prime factors of 31149 are 3, 3461. Prime factorization of 31149 in exponential form is:

31149 = 3² × 3461¹

Step-3: Factors of 31140

List of positive integer factors of 31140 that divides 31140 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 173, 180, 346, 519, 692, 865, 1038, 1557, 1730, 2076, 2595, 3114, 3460, 5190, 6228, 7785, 10380, 15570

Step-4: Factors of 31149

List of positive integer factors of 31149 that divides 31140 without a remainder.

1, 3, 9, 3461, 10383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31140 and 31149. The biggest common factor number is the GCF number.
So the greatest common factor 31140 and 31149 is 9.

Also check out the Least Common Multiple of 31140 and 31149