What is the Greatest Common Factor of 31766 and 31780?

Greatest common factor (GCF) of 31766 and 31780 is 14.

GCF(31766,31780) = 14

We will now calculate the prime factors of 31766 and 31780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31766 and 31780.

How to find the GCF of 31766 and 31780?

We will first find the prime factorization of 31766 and 31780. After we will calculate the factors of 31766 and 31780 and find the biggest common factor number .

Step-1: Prime Factorization of 31766

Prime factors of 31766 are 2, 7, 2269. Prime factorization of 31766 in exponential form is:

31766 = 2¹ × 7¹ × 2269¹

Step-2: Prime Factorization of 31780

Prime factors of 31780 are 2, 5, 7, 227. Prime factorization of 31780 in exponential form is:

31780 = 2² × 5¹ × 7¹ × 227¹

Step-3: Factors of 31766

List of positive integer factors of 31766 that divides 31766 without a remainder.

1, 2, 7, 14, 2269, 4538, 15883

Step-4: Factors of 31780

List of positive integer factors of 31780 that divides 31766 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 227, 454, 908, 1135, 1589, 2270, 3178, 4540, 6356, 7945, 15890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31766 and 31780. The biggest common factor number is the GCF number.
So the greatest common factor 31766 and 31780 is 14.

Also check out the Least Common Multiple of 31766 and 31780