What is the Greatest Common Factor of 83184 and 83204?

Greatest common factor (GCF) of 83184 and 83204 is 4.

GCF(83184,83204) = 4

We will now calculate the prime factors of 83184 and 83204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83184 and 83204.

How to find the GCF of 83184 and 83204?

We will first find the prime factorization of 83184 and 83204. After we will calculate the factors of 83184 and 83204 and find the biggest common factor number .

Step-1: Prime Factorization of 83184

Prime factors of 83184 are 2, 3, 1733. Prime factorization of 83184 in exponential form is:

83184 = 2⁴ × 3¹ × 1733¹

Step-2: Prime Factorization of 83204

Prime factors of 83204 are 2, 11, 31, 61. Prime factorization of 83204 in exponential form is:

83204 = 2² × 11¹ × 31¹ × 61¹

Step-3: Factors of 83184

List of positive integer factors of 83184 that divides 83184 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1733, 3466, 5199, 6932, 10398, 13864, 20796, 27728, 41592

Step-4: Factors of 83204

List of positive integer factors of 83204 that divides 83184 without a remainder.

1, 2, 4, 11, 22, 31, 44, 61, 62, 122, 124, 244, 341, 671, 682, 1342, 1364, 1891, 2684, 3782, 7564, 20801, 41602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83184 and 83204. The biggest common factor number is the GCF number.
So the greatest common factor 83184 and 83204 is 4.

Also check out the Least Common Multiple of 83184 and 83204