What is the Greatest Common Factor of 31149 and 31164?

Greatest common factor (GCF) of 31149 and 31164 is 3.

GCF(31149,31164) = 3

We will now calculate the prime factors of 31149 and 31164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31149 and 31164.

How to find the GCF of 31149 and 31164?

We will first find the prime factorization of 31149 and 31164. After we will calculate the factors of 31149 and 31164 and find the biggest common factor number .

Step-1: Prime Factorization of 31149

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

31149 = 3² × 3461¹

Step-2: Prime Factorization of 31164

Prime factors of 31164 are 2, 3, 7, 53. Prime factorization of 31164 in exponential form is:

31164 = 2² × 3¹ × 7² × 53¹

Step-3: Factors of 31149

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

1, 3, 9, 3461, 10383

Step-4: Factors of 31164

List of positive integer factors of 31164 that divides 31149 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 53, 84, 98, 106, 147, 159, 196, 212, 294, 318, 371, 588, 636, 742, 1113, 1484, 2226, 2597, 4452, 5194, 7791, 10388, 15582

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31149 and 31164. The biggest common factor number is the GCF number.
So the greatest common factor 31149 and 31164 is 3.

Also check out the Least Common Multiple of 31149 and 31164