What is the Greatest Common Factor of 34380 and 34400?

Greatest common factor (GCF) of 34380 and 34400 is 20.

GCF(34380,34400) = 20

We will now calculate the prime factors of 34380 and 34400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34380 and 34400.

How to find the GCF of 34380 and 34400?

We will first find the prime factorization of 34380 and 34400. After we will calculate the factors of 34380 and 34400 and find the biggest common factor number .

Step-1: Prime Factorization of 34380

Prime factors of 34380 are 2, 3, 5, 191. Prime factorization of 34380 in exponential form is:

34380 = 2² × 3² × 5¹ × 191¹

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 34380

List of positive integer factors of 34380 that divides 34380 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 191, 382, 573, 764, 955, 1146, 1719, 1910, 2292, 2865, 3438, 3820, 5730, 6876, 8595, 11460, 17190

Step-4: Factors of 34400

List of positive integer factors of 34400 that divides 34380 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 34380 and 34400. The biggest common factor number is the GCF number.
So the greatest common factor 34380 and 34400 is 20.

Also check out the Least Common Multiple of 34380 and 34400