What is the Greatest Common Factor of 31365 and 31374?

Greatest common factor (GCF) of 31365 and 31374 is 9.

GCF(31365,31374) = 9

We will now calculate the prime factors of 31365 and 31374, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31365 and 31374.

How to find the GCF of 31365 and 31374?

We will first find the prime factorization of 31365 and 31374. After we will calculate the factors of 31365 and 31374 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 31374

Prime factors of 31374 are 2, 3, 7, 83. Prime factorization of 31374 in exponential form is:

31374 = 2¹ × 3³ × 7¹ × 83¹

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 31374

List of positive integer factors of 31374 that divides 31365 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 83, 126, 166, 189, 249, 378, 498, 581, 747, 1162, 1494, 1743, 2241, 3486, 4482, 5229, 10458, 15687

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31365 and 31374. The biggest common factor number is the GCF number.
So the greatest common factor 31365 and 31374 is 9.

Also check out the Least Common Multiple of 31365 and 31374