What is the Greatest Common Factor of 34400 and 34419?

Greatest common factor (GCF) of 34400 and 34419 is 1.

GCF(34400,34419) = 1

We will now calculate the prime factors of 34400 and 34419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34400 and 34419.

How to find the GCF of 34400 and 34419?

We will first find the prime factorization of 34400 and 34419. After we will calculate the factors of 34400 and 34419 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 34419

Prime factors of 34419 are 3, 7, 11, 149. Prime factorization of 34419 in exponential form is:

34419 = 3¹ × 7¹ × 11¹ × 149¹

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 34419

List of positive integer factors of 34419 that divides 34400 without a remainder.

1, 3, 7, 11, 21, 33, 77, 149, 231, 447, 1043, 1639, 3129, 4917, 11473

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34400 and 34419. The biggest common factor number is the GCF number.
So the greatest common factor 34400 and 34419 is 1.

Also check out the Least Common Multiple of 34400 and 34419