What is the Greatest Common Factor of 82194 and 82200?

Greatest common factor (GCF) of 82194 and 82200 is 6.

GCF(82194,82200) = 6

We will now calculate the prime factors of 82194 and 82200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82194 and 82200.

How to find the GCF of 82194 and 82200?

We will first find the prime factorization of 82194 and 82200. After we will calculate the factors of 82194 and 82200 and find the biggest common factor number .

Step-1: Prime Factorization of 82194

Prime factors of 82194 are 2, 3, 7, 19, 103. Prime factorization of 82194 in exponential form is:

82194 = 2¹ × 3¹ × 7¹ × 19¹ × 103¹

Step-2: 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-3: Factors of 82194

List of positive integer factors of 82194 that divides 82194 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 103, 114, 133, 206, 266, 309, 399, 618, 721, 798, 1442, 1957, 2163, 3914, 4326, 5871, 11742, 13699, 27398, 41097

Step-4: Factors of 82200

List of positive integer factors of 82200 that divides 82194 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82194 and 82200. The biggest common factor number is the GCF number.
So the greatest common factor 82194 and 82200 is 6.

Also check out the Least Common Multiple of 82194 and 82200