What is the Greatest Common Factor of 34400 and 34415?

Greatest common factor (GCF) of 34400 and 34415 is 5.

GCF(34400,34415) = 5

We will now calculate the prime factors of 34400 and 34415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34400 and 34415.

How to find the GCF of 34400 and 34415?

We will first find the prime factorization of 34400 and 34415. After we will calculate the factors of 34400 and 34415 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34415

Prime factors of 34415 are 5, 6883. Prime factorization of 34415 in exponential form is:

34415 = 5¹ × 6883¹

Step-3: Factors of 34400

List of positive integer factors of 34400 that divides 34400 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

Step-4: Factors of 34415

List of positive integer factors of 34415 that divides 34400 without a remainder.

1, 5, 6883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34400 and 34415. The biggest common factor number is the GCF number.
So the greatest common factor 34400 and 34415 is 5.

Also check out the Least Common Multiple of 34400 and 34415