What is the Greatest Common Factor of 31700 and 31720?

Greatest common factor (GCF) of 31700 and 31720 is 20.

GCF(31700,31720) = 20

We will now calculate the prime factors of 31700 and 31720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31700 and 31720.

How to find the GCF of 31700 and 31720?

We will first find the prime factorization of 31700 and 31720. After we will calculate the factors of 31700 and 31720 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31720

Prime factors of 31720 are 2, 5, 13, 61. Prime factorization of 31720 in exponential form is:

31720 = 2³ × 5¹ × 13¹ × 61¹

Step-3: Factors of 31700

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

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

Step-4: Factors of 31720

List of positive integer factors of 31720 that divides 31700 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 61, 65, 104, 122, 130, 244, 260, 305, 488, 520, 610, 793, 1220, 1586, 2440, 3172, 3965, 6344, 7930, 15860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31700 and 31720. The biggest common factor number is the GCF number.
So the greatest common factor 31700 and 31720 is 20.

Also check out the Least Common Multiple of 31700 and 31720