What is the Greatest Common Factor of 31365 and 31382?

Greatest common factor (GCF) of 31365 and 31382 is 17.

GCF(31365,31382) = 17

We will now calculate the prime factors of 31365 and 31382, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31365 and 31382.

How to find the GCF of 31365 and 31382?

We will first find the prime factorization of 31365 and 31382. After we will calculate the factors of 31365 and 31382 and find the biggest common factor number .

Step-1: Prime Factorization of 31365

Prime factors of 31365 are 3, 5, 17, 41. Prime factorization of 31365 in exponential form is:

31365 = 3² × 5¹ × 17¹ × 41¹

Step-2: Prime Factorization of 31382

Prime factors of 31382 are 2, 13, 17, 71. Prime factorization of 31382 in exponential form is:

31382 = 2¹ × 13¹ × 17¹ × 71¹

Step-3: Factors of 31365

List of positive integer factors of 31365 that divides 31365 without a remainder.

1, 3, 5, 9, 15, 17, 41, 45, 51, 85, 123, 153, 205, 255, 369, 615, 697, 765, 1845, 2091, 3485, 6273, 10455

Step-4: Factors of 31382

List of positive integer factors of 31382 that divides 31365 without a remainder.

1, 2, 13, 17, 26, 34, 71, 142, 221, 442, 923, 1207, 1846, 2414, 15691

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31365 and 31382. The biggest common factor number is the GCF number.
So the greatest common factor 31365 and 31382 is 17.

Also check out the Least Common Multiple of 31365 and 31382