What is the Greatest Common Factor of 19278 and 19296?

Greatest common factor (GCF) of 19278 and 19296 is 18.

GCF(19278,19296) = 18

We will now calculate the prime factors of 19278 and 19296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19278 and 19296.

How to find the GCF of 19278 and 19296?

We will first find the prime factorization of 19278 and 19296. After we will calculate the factors of 19278 and 19296 and find the biggest common factor number .

Step-1: Prime Factorization of 19278

Prime factors of 19278 are 2, 3, 7, 17. Prime factorization of 19278 in exponential form is:

19278 = 2¹ × 3⁴ × 7¹ × 17¹

Step-2: Prime Factorization of 19296

Prime factors of 19296 are 2, 3, 67. Prime factorization of 19296 in exponential form is:

19296 = 2⁵ × 3² × 67¹

Step-3: Factors of 19278

List of positive integer factors of 19278 that divides 19278 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 27, 34, 42, 51, 54, 63, 81, 102, 119, 126, 153, 162, 189, 238, 306, 357, 378, 459, 567, 714, 918, 1071, 1134, 1377, 2142, 2754, 3213, 6426, 9639

Step-4: Factors of 19296

List of positive integer factors of 19296 that divides 19278 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 67, 72, 96, 134, 144, 201, 268, 288, 402, 536, 603, 804, 1072, 1206, 1608, 2144, 2412, 3216, 4824, 6432, 9648

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19278 and 19296. The biggest common factor number is the GCF number.
So the greatest common factor 19278 and 19296 is 18.

Also check out the Least Common Multiple of 19278 and 19296