What is the Greatest Common Factor of 31293 and 31312?

Greatest common factor (GCF) of 31293 and 31312 is 19.

GCF(31293,31312) = 19

We will now calculate the prime factors of 31293 and 31312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31293 and 31312.

How to find the GCF of 31293 and 31312?

We will first find the prime factorization of 31293 and 31312. After we will calculate the factors of 31293 and 31312 and find the biggest common factor number .

Step-1: Prime Factorization of 31293

Prime factors of 31293 are 3, 19, 61. Prime factorization of 31293 in exponential form is:

31293 = 3³ × 19¹ × 61¹

Step-2: Prime Factorization of 31312

Prime factors of 31312 are 2, 19, 103. Prime factorization of 31312 in exponential form is:

31312 = 2⁴ × 19¹ × 103¹

Step-3: Factors of 31293

List of positive integer factors of 31293 that divides 31293 without a remainder.

1, 3, 9, 19, 27, 57, 61, 171, 183, 513, 549, 1159, 1647, 3477, 10431

Step-4: Factors of 31312

List of positive integer factors of 31312 that divides 31293 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 103, 152, 206, 304, 412, 824, 1648, 1957, 3914, 7828, 15656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31293 and 31312. The biggest common factor number is the GCF number.
So the greatest common factor 31293 and 31312 is 19.

Also check out the Least Common Multiple of 31293 and 31312