What is the Greatest Common Factor of 34385 and 34398?

Greatest common factor (GCF) of 34385 and 34398 is 13.

GCF(34385,34398) = 13

We will now calculate the prime factors of 34385 and 34398, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34385 and 34398.

How to find the GCF of 34385 and 34398?

We will first find the prime factorization of 34385 and 34398. After we will calculate the factors of 34385 and 34398 and find the biggest common factor number .

Step-1: Prime Factorization of 34385

Prime factors of 34385 are 5, 13, 23. Prime factorization of 34385 in exponential form is:

34385 = 5¹ × 13¹ × 23²

Step-2: Prime Factorization of 34398

Prime factors of 34398 are 2, 3, 7, 13. Prime factorization of 34398 in exponential form is:

34398 = 2¹ × 3³ × 7² × 13¹

Step-3: Factors of 34385

List of positive integer factors of 34385 that divides 34385 without a remainder.

1, 5, 13, 23, 65, 115, 299, 529, 1495, 2645, 6877

Step-4: Factors of 34398

List of positive integer factors of 34398 that divides 34385 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 49, 54, 63, 78, 91, 98, 117, 126, 147, 182, 189, 234, 273, 294, 351, 378, 441, 546, 637, 702, 819, 882, 1274, 1323, 1638, 1911, 2457, 2646, 3822, 4914, 5733, 11466, 17199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34385 and 34398. The biggest common factor number is the GCF number.
So the greatest common factor 34385 and 34398 is 13.

Also check out the Least Common Multiple of 34385 and 34398