What is the Greatest Common Factor of 82200 and 82208?

Greatest common factor (GCF) of 82200 and 82208 is 8.

GCF(82200,82208) = 8

We will now calculate the prime factors of 82200 and 82208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82200 and 82208.

How to find the GCF of 82200 and 82208?

We will first find the prime factorization of 82200 and 82208. After we will calculate the factors of 82200 and 82208 and find the biggest common factor number .

Step-1: Prime Factorization of 82200

Prime factors of 82200 are 2, 3, 5, 137. Prime factorization of 82200 in exponential form is:

82200 = 2³ × 3¹ × 5² × 137¹

Step-2: Prime Factorization of 82208

Prime factors of 82208 are 2, 7, 367. Prime factorization of 82208 in exponential form is:

82208 = 2⁵ × 7¹ × 367¹

Step-3: Factors of 82200

List of positive integer factors of 82200 that divides 82200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 137, 150, 200, 274, 300, 411, 548, 600, 685, 822, 1096, 1370, 1644, 2055, 2740, 3288, 3425, 4110, 5480, 6850, 8220, 10275, 13700, 16440, 20550, 27400, 41100

Step-4: Factors of 82208

List of positive integer factors of 82208 that divides 82200 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 367, 734, 1468, 2569, 2936, 5138, 5872, 10276, 11744, 20552, 41104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82200 and 82208. The biggest common factor number is the GCF number.
So the greatest common factor 82200 and 82208 is 8.

Also check out the Least Common Multiple of 82200 and 82208