What is the Greatest Common Factor of 38184 and 38200?

Greatest common factor (GCF) of 38184 and 38200 is 8.

GCF(38184,38200) = 8

We will now calculate the prime factors of 38184 and 38200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38184 and 38200.

How to find the GCF of 38184 and 38200?

We will first find the prime factorization of 38184 and 38200. After we will calculate the factors of 38184 and 38200 and find the biggest common factor number .

Step-1: Prime Factorization of 38184

Prime factors of 38184 are 2, 3, 37, 43. Prime factorization of 38184 in exponential form is:

38184 = 2³ × 3¹ × 37¹ × 43¹

Step-2: Prime Factorization of 38200

Prime factors of 38200 are 2, 5, 191. Prime factorization of 38200 in exponential form is:

38200 = 2³ × 5² × 191¹

Step-3: Factors of 38184

List of positive integer factors of 38184 that divides 38184 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 37, 43, 74, 86, 111, 129, 148, 172, 222, 258, 296, 344, 444, 516, 888, 1032, 1591, 3182, 4773, 6364, 9546, 12728, 19092

Step-4: Factors of 38200

List of positive integer factors of 38200 that divides 38184 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 191, 200, 382, 764, 955, 1528, 1910, 3820, 4775, 7640, 9550, 19100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38184 and 38200. The biggest common factor number is the GCF number.
So the greatest common factor 38184 and 38200 is 8.

Also check out the Least Common Multiple of 38184 and 38200