What is the Greatest Common Factor of 31164 and 31178?

Greatest common factor (GCF) of 31164 and 31178 is 14.

GCF(31164,31178) = 14

We will now calculate the prime factors of 31164 and 31178, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31164 and 31178.

How to find the GCF of 31164 and 31178?

We will first find the prime factorization of 31164 and 31178. After we will calculate the factors of 31164 and 31178 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31178

Prime factors of 31178 are 2, 7, 17, 131. Prime factorization of 31178 in exponential form is:

31178 = 2¹ × 7¹ × 17¹ × 131¹

Step-3: Factors of 31164

List of positive integer factors of 31164 that divides 31164 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

Step-4: Factors of 31178

List of positive integer factors of 31178 that divides 31164 without a remainder.

1, 2, 7, 14, 17, 34, 119, 131, 238, 262, 917, 1834, 2227, 4454, 15589

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31164 and 31178. The biggest common factor number is the GCF number.
So the greatest common factor 31164 and 31178 is 14.

Also check out the Least Common Multiple of 31164 and 31178