What is the Greatest Common Factor of 34395 and 34400?

Greatest common factor (GCF) of 34395 and 34400 is 5.

GCF(34395,34400) = 5

We will now calculate the prime factors of 34395 and 34400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34395 and 34400.

How to find the GCF of 34395 and 34400?

We will first find the prime factorization of 34395 and 34400. After we will calculate the factors of 34395 and 34400 and find the biggest common factor number .

Step-1: Prime Factorization of 34395

Prime factors of 34395 are 3, 5, 2293. Prime factorization of 34395 in exponential form is:

34395 = 3¹ × 5¹ × 2293¹

Step-2: Prime Factorization of 34400

Prime factors of 34400 are 2, 5, 43. Prime factorization of 34400 in exponential form is:

34400 = 2⁵ × 5² × 43¹

Step-3: Factors of 34395

List of positive integer factors of 34395 that divides 34395 without a remainder.

1, 3, 5, 15, 2293, 6879, 11465

Step-4: Factors of 34400

List of positive integer factors of 34400 that divides 34395 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 43, 50, 80, 86, 100, 160, 172, 200, 215, 344, 400, 430, 688, 800, 860, 1075, 1376, 1720, 2150, 3440, 4300, 6880, 8600, 17200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34395 and 34400. The biggest common factor number is the GCF number.
So the greatest common factor 34395 and 34400 is 5.

Also check out the Least Common Multiple of 34395 and 34400