What is the Greatest Common Factor of 31766 and 31772?

Greatest common factor (GCF) of 31766 and 31772 is 2.

GCF(31766,31772) = 2

We will now calculate the prime factors of 31766 and 31772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31766 and 31772.

How to find the GCF of 31766 and 31772?

We will first find the prime factorization of 31766 and 31772. After we will calculate the factors of 31766 and 31772 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 31772

Prime factors of 31772 are 2, 13, 47. Prime factorization of 31772 in exponential form is:

31772 = 2² × 13² × 47¹

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 31772

List of positive integer factors of 31772 that divides 31766 without a remainder.

1, 2, 4, 13, 26, 47, 52, 94, 169, 188, 338, 611, 676, 1222, 2444, 7943, 15886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31766 and 31772. The biggest common factor number is the GCF number.
So the greatest common factor 31766 and 31772 is 2.

Also check out the Least Common Multiple of 31766 and 31772