What is the Greatest Common Factor of 82384 and 82400?

Greatest common factor (GCF) of 82384 and 82400 is 16.

GCF(82384,82400) = 16

We will now calculate the prime factors of 82384 and 82400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82384 and 82400.

How to find the GCF of 82384 and 82400?

We will first find the prime factorization of 82384 and 82400. After we will calculate the factors of 82384 and 82400 and find the biggest common factor number .

Step-1: Prime Factorization of 82384

Prime factors of 82384 are 2, 19, 271. Prime factorization of 82384 in exponential form is:

82384 = 2⁴ × 19¹ × 271¹

Step-2: Prime Factorization of 82400

Prime factors of 82400 are 2, 5, 103. Prime factorization of 82400 in exponential form is:

82400 = 2⁵ × 5² × 103¹

Step-3: Factors of 82384

List of positive integer factors of 82384 that divides 82384 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 271, 304, 542, 1084, 2168, 4336, 5149, 10298, 20596, 41192

Step-4: Factors of 82400

List of positive integer factors of 82400 that divides 82384 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 103, 160, 200, 206, 400, 412, 515, 800, 824, 1030, 1648, 2060, 2575, 3296, 4120, 5150, 8240, 10300, 16480, 20600, 41200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82384 and 82400. The biggest common factor number is the GCF number.
So the greatest common factor 82384 and 82400 is 16.

Also check out the Least Common Multiple of 82384 and 82400