What is the Greatest Common Factor of 31290 and 31304?

Greatest common factor (GCF) of 31290 and 31304 is 14.

GCF(31290,31304) = 14

We will now calculate the prime factors of 31290 and 31304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31290 and 31304.

How to find the GCF of 31290 and 31304?

We will first find the prime factorization of 31290 and 31304. After we will calculate the factors of 31290 and 31304 and find the biggest common factor number .

Step-1: Prime Factorization of 31290

Prime factors of 31290 are 2, 3, 5, 7, 149. Prime factorization of 31290 in exponential form is:

31290 = 2¹ × 3¹ × 5¹ × 7¹ × 149¹

Step-2: Prime Factorization of 31304

Prime factors of 31304 are 2, 7, 13, 43. Prime factorization of 31304 in exponential form is:

31304 = 2³ × 7¹ × 13¹ × 43¹

Step-3: Factors of 31290

List of positive integer factors of 31290 that divides 31290 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 149, 210, 298, 447, 745, 894, 1043, 1490, 2086, 2235, 3129, 4470, 5215, 6258, 10430, 15645

Step-4: Factors of 31304

List of positive integer factors of 31304 that divides 31290 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 43, 52, 56, 86, 91, 104, 172, 182, 301, 344, 364, 559, 602, 728, 1118, 1204, 2236, 2408, 3913, 4472, 7826, 15652

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31290 and 31304. The biggest common factor number is the GCF number.
So the greatest common factor 31290 and 31304 is 14.

Also check out the Least Common Multiple of 31290 and 31304