What is the Greatest Common Factor of 19104 and 19110?

Greatest common factor (GCF) of 19104 and 19110 is 6.

GCF(19104,19110) = 6

We will now calculate the prime factors of 19104 and 19110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19104 and 19110.

How to find the GCF of 19104 and 19110?

We will first find the prime factorization of 19104 and 19110. After we will calculate the factors of 19104 and 19110 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 19110

Prime factors of 19110 are 2, 3, 5, 7, 13. Prime factorization of 19110 in exponential form is:

19110 = 2¹ × 3¹ × 5¹ × 7² × 13¹

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 19110

List of positive integer factors of 19110 that divides 19104 without a remainder.

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 49, 65, 70, 78, 91, 98, 105, 130, 147, 182, 195, 210, 245, 273, 294, 390, 455, 490, 546, 637, 735, 910, 1274, 1365, 1470, 1911, 2730, 3185, 3822, 6370, 9555

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19104 and 19110. The biggest common factor number is the GCF number.
So the greatest common factor 19104 and 19110 is 6.

Also check out the Least Common Multiple of 19104 and 19110