What is the Greatest Common Factor of 19104 and 19116?

Greatest common factor (GCF) of 19104 and 19116 is 12.

GCF(19104,19116) = 12

We will now calculate the prime factors of 19104 and 19116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19104 and 19116.

How to find the GCF of 19104 and 19116?

We will first find the prime factorization of 19104 and 19116. After we will calculate the factors of 19104 and 19116 and find the biggest common factor number .

Step-1: Prime Factorization of 19104

Prime factors of 19104 are 2, 3, 199. Prime factorization of 19104 in exponential form is:

19104 = 2⁵ × 3¹ × 199¹

Step-2: Prime Factorization of 19116

Prime factors of 19116 are 2, 3, 59. Prime factorization of 19116 in exponential form is:

19116 = 2² × 3⁴ × 59¹

Step-3: Factors of 19104

List of positive integer factors of 19104 that divides 19104 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 199, 398, 597, 796, 1194, 1592, 2388, 3184, 4776, 6368, 9552

Step-4: Factors of 19116

List of positive integer factors of 19116 that divides 19104 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 59, 81, 108, 118, 162, 177, 236, 324, 354, 531, 708, 1062, 1593, 2124, 3186, 4779, 6372, 9558

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19104 and 19116. The biggest common factor number is the GCF number.
So the greatest common factor 19104 and 19116 is 12.

Also check out the Least Common Multiple of 19104 and 19116