What is the Greatest Common Factor of 31772 and 31785?

Greatest common factor (GCF) of 31772 and 31785 is 13.

GCF(31772,31785) = 13

We will now calculate the prime factors of 31772 and 31785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31772 and 31785.

How to find the GCF of 31772 and 31785?

We will first find the prime factorization of 31772 and 31785. After we will calculate the factors of 31772 and 31785 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31785

Prime factors of 31785 are 3, 5, 13, 163. Prime factorization of 31785 in exponential form is:

31785 = 3¹ × 5¹ × 13¹ × 163¹

Step-3: Factors of 31772

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

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

Step-4: Factors of 31785

List of positive integer factors of 31785 that divides 31772 without a remainder.

1, 3, 5, 13, 15, 39, 65, 163, 195, 489, 815, 2119, 2445, 6357, 10595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31772 and 31785. The biggest common factor number is the GCF number.
So the greatest common factor 31772 and 31785 is 13.

Also check out the Least Common Multiple of 31772 and 31785