What is the Greatest Common Factor of 23184 and 23198?

Greatest common factor (GCF) of 23184 and 23198 is 14.

GCF(23184,23198) = 14

We will now calculate the prime factors of 23184 and 23198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23184 and 23198.

How to find the GCF of 23184 and 23198?

We will first find the prime factorization of 23184 and 23198. After we will calculate the factors of 23184 and 23198 and find the biggest common factor number .

Step-1: Prime Factorization of 23184

Prime factors of 23184 are 2, 3, 7, 23. Prime factorization of 23184 in exponential form is:

23184 = 2⁴ × 3² × 7¹ × 23¹

Step-2: Prime Factorization of 23198

Prime factors of 23198 are 2, 7, 1657. Prime factorization of 23198 in exponential form is:

23198 = 2¹ × 7¹ × 1657¹

Step-3: Factors of 23184

List of positive integer factors of 23184 that divides 23184 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 23, 24, 28, 36, 42, 46, 48, 56, 63, 69, 72, 84, 92, 112, 126, 138, 144, 161, 168, 184, 207, 252, 276, 322, 336, 368, 414, 483, 504, 552, 644, 828, 966, 1008, 1104, 1288, 1449, 1656, 1932, 2576, 2898, 3312, 3864, 5796, 7728, 11592

Step-4: Factors of 23198

List of positive integer factors of 23198 that divides 23184 without a remainder.

1, 2, 7, 14, 1657, 3314, 11599

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23184 and 23198. The biggest common factor number is the GCF number.
So the greatest common factor 23184 and 23198 is 14.

Also check out the Least Common Multiple of 23184 and 23198