What is the Greatest Common Factor of 19344 and 19360?

Greatest common factor (GCF) of 19344 and 19360 is 16.

GCF(19344,19360) = 16

We will now calculate the prime factors of 19344 and 19360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19344 and 19360.

How to find the GCF of 19344 and 19360?

We will first find the prime factorization of 19344 and 19360. After we will calculate the factors of 19344 and 19360 and find the biggest common factor number .

Step-1: Prime Factorization of 19344

Prime factors of 19344 are 2, 3, 13, 31. Prime factorization of 19344 in exponential form is:

19344 = 2⁴ × 3¹ × 13¹ × 31¹

Step-2: Prime Factorization of 19360

Prime factors of 19360 are 2, 5, 11. Prime factorization of 19360 in exponential form is:

19360 = 2⁵ × 5¹ × 11²

Step-3: Factors of 19344

List of positive integer factors of 19344 that divides 19344 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 39, 48, 52, 62, 78, 93, 104, 124, 156, 186, 208, 248, 312, 372, 403, 496, 624, 744, 806, 1209, 1488, 1612, 2418, 3224, 4836, 6448, 9672

Step-4: Factors of 19360

List of positive integer factors of 19360 that divides 19344 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 121, 160, 176, 220, 242, 352, 440, 484, 605, 880, 968, 1210, 1760, 1936, 2420, 3872, 4840, 9680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19344 and 19360. The biggest common factor number is the GCF number.
So the greatest common factor 19344 and 19360 is 16.

Also check out the Least Common Multiple of 19344 and 19360