What is the Greatest Common Factor of 34314 and 34323?

Greatest common factor (GCF) of 34314 and 34323 is 3.

GCF(34314,34323) = 3

We will now calculate the prime factors of 34314 and 34323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34314 and 34323.

How to find the GCF of 34314 and 34323?

We will first find the prime factorization of 34314 and 34323. After we will calculate the factors of 34314 and 34323 and find the biggest common factor number .

Step-1: Prime Factorization of 34314

Prime factors of 34314 are 2, 3, 7, 19, 43. Prime factorization of 34314 in exponential form is:

34314 = 2¹ × 3¹ × 7¹ × 19¹ × 43¹

Step-2: Prime Factorization of 34323

Prime factors of 34323 are 3, 17, 673. Prime factorization of 34323 in exponential form is:

34323 = 3¹ × 17¹ × 673¹

Step-3: Factors of 34314

List of positive integer factors of 34314 that divides 34314 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 43, 57, 86, 114, 129, 133, 258, 266, 301, 399, 602, 798, 817, 903, 1634, 1806, 2451, 4902, 5719, 11438, 17157

Step-4: Factors of 34323

List of positive integer factors of 34323 that divides 34314 without a remainder.

1, 3, 17, 51, 673, 2019, 11441

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34314 and 34323. The biggest common factor number is the GCF number.
So the greatest common factor 34314 and 34323 is 3.

Also check out the Least Common Multiple of 34314 and 34323