What is the Greatest Common Factor of 31709 and 31720?

Greatest common factor (GCF) of 31709 and 31720 is 1.

GCF(31709,31720) = 1

We will now calculate the prime factors of 31709 and 31720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31709 and 31720.

How to find the GCF of 31709 and 31720?

We will first find the prime factorization of 31709 and 31720. After we will calculate the factors of 31709 and 31720 and find the biggest common factor number .

Step-1: Prime Factorization of 31709

Prime factors of 31709 are 37, 857. Prime factorization of 31709 in exponential form is:

31709 = 37¹ × 857¹

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 31709

List of positive integer factors of 31709 that divides 31709 without a remainder.

1, 37, 857

Step-4: Factors of 31720

List of positive integer factors of 31720 that divides 31709 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 31709 and 31720. The biggest common factor number is the GCF number.
So the greatest common factor 31709 and 31720 is 1.

Also check out the Least Common Multiple of 31709 and 31720