What is the Greatest Common Factor of 32184 and 32200?

Greatest common factor (GCF) of 32184 and 32200 is 8.

GCF(32184,32200) = 8

We will now calculate the prime factors of 32184 and 32200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32184 and 32200.

How to find the GCF of 32184 and 32200?

We will first find the prime factorization of 32184 and 32200. After we will calculate the factors of 32184 and 32200 and find the biggest common factor number .

Step-1: Prime Factorization of 32184

Prime factors of 32184 are 2, 3, 149. Prime factorization of 32184 in exponential form is:

32184 = 2³ × 3³ × 149¹

Step-2: Prime Factorization of 32200

Prime factors of 32200 are 2, 5, 7, 23. Prime factorization of 32200 in exponential form is:

32200 = 2³ × 5² × 7¹ × 23¹

Step-3: Factors of 32184

List of positive integer factors of 32184 that divides 32184 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 149, 216, 298, 447, 596, 894, 1192, 1341, 1788, 2682, 3576, 4023, 5364, 8046, 10728, 16092

Step-4: Factors of 32200

List of positive integer factors of 32200 that divides 32184 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 92, 100, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 460, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 2300, 3220, 4025, 4600, 6440, 8050, 16100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32184 and 32200. The biggest common factor number is the GCF number.
So the greatest common factor 32184 and 32200 is 8.

Also check out the Least Common Multiple of 32184 and 32200