What is the Greatest Common Factor of 31688 and 31700?

Greatest common factor (GCF) of 31688 and 31700 is 4.

GCF(31688,31700) = 4

We will now calculate the prime factors of 31688 and 31700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31688 and 31700.

How to find the GCF of 31688 and 31700?

We will first find the prime factorization of 31688 and 31700. After we will calculate the factors of 31688 and 31700 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31700

Prime factors of 31700 are 2, 5, 317. Prime factorization of 31700 in exponential form is:

31700 = 2² × 5² × 317¹

Step-3: Factors of 31688

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

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

Step-4: Factors of 31700

List of positive integer factors of 31700 that divides 31688 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 317, 634, 1268, 1585, 3170, 6340, 7925, 15850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31688 and 31700. The biggest common factor number is the GCF number.
So the greatest common factor 31688 and 31700 is 4.

Also check out the Least Common Multiple of 31688 and 31700