What is the Greatest Common Factor of 31671 and 31688?

Greatest common factor (GCF) of 31671 and 31688 is 17.

GCF(31671,31688) = 17

We will now calculate the prime factors of 31671 and 31688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31671 and 31688.

How to find the GCF of 31671 and 31688?

We will first find the prime factorization of 31671 and 31688. After we will calculate the factors of 31671 and 31688 and find the biggest common factor number .

Step-1: Prime Factorization of 31671

Prime factors of 31671 are 3, 17, 23. Prime factorization of 31671 in exponential form is:

31671 = 3⁴ × 17¹ × 23¹

Step-2: Prime Factorization of 31688

Prime factors of 31688 are 2, 17, 233. Prime factorization of 31688 in exponential form is:

31688 = 2³ × 17¹ × 233¹

Step-3: Factors of 31671

List of positive integer factors of 31671 that divides 31671 without a remainder.

1, 3, 9, 17, 23, 27, 51, 69, 81, 153, 207, 391, 459, 621, 1173, 1377, 1863, 3519, 10557

Step-4: Factors of 31688

List of positive integer factors of 31688 that divides 31671 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 233, 466, 932, 1864, 3961, 7922, 15844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31671 and 31688. The biggest common factor number is the GCF number.
So the greatest common factor 31671 and 31688 is 17.

Also check out the Least Common Multiple of 31671 and 31688