What is the Greatest Common Factor of 31760 and 31766?

Greatest common factor (GCF) of 31760 and 31766 is 2.

GCF(31760,31766) = 2

We will now calculate the prime factors of 31760 and 31766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31760 and 31766.

How to find the GCF of 31760 and 31766?

We will first find the prime factorization of 31760 and 31766. After we will calculate the factors of 31760 and 31766 and find the biggest common factor number .

Step-1: Prime Factorization of 31760

Prime factors of 31760 are 2, 5, 397. Prime factorization of 31760 in exponential form is:

31760 = 2⁴ × 5¹ × 397¹

Step-2: 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-3: Factors of 31760

List of positive integer factors of 31760 that divides 31760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 397, 794, 1588, 1985, 3176, 3970, 6352, 7940, 15880

Step-4: Factors of 31766

List of positive integer factors of 31766 that divides 31760 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31760 and 31766. The biggest common factor number is the GCF number.
So the greatest common factor 31760 and 31766 is 2.

Also check out the Least Common Multiple of 31760 and 31766