What is the Greatest Common Factor of 31297 and 31304?

Greatest common factor (GCF) of 31297 and 31304 is 7.

GCF(31297,31304) = 7

We will now calculate the prime factors of 31297 and 31304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31297 and 31304.

How to find the GCF of 31297 and 31304?

We will first find the prime factorization of 31297 and 31304. After we will calculate the factors of 31297 and 31304 and find the biggest common factor number .

Step-1: Prime Factorization of 31297

Prime factors of 31297 are 7, 17, 263. Prime factorization of 31297 in exponential form is:

31297 = 7¹ × 17¹ × 263¹

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 31297

List of positive integer factors of 31297 that divides 31297 without a remainder.

1, 7, 17, 119, 263, 1841, 4471

Step-4: Factors of 31304

List of positive integer factors of 31304 that divides 31297 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 31297 and 31304. The biggest common factor number is the GCF number.
So the greatest common factor 31297 and 31304 is 7.

Also check out the Least Common Multiple of 31297 and 31304