What is the Greatest Common Factor of 19488 and 19504?

Greatest common factor (GCF) of 19488 and 19504 is 16.

GCF(19488,19504) = 16

We will now calculate the prime factors of 19488 and 19504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19488 and 19504.

How to find the GCF of 19488 and 19504?

We will first find the prime factorization of 19488 and 19504. After we will calculate the factors of 19488 and 19504 and find the biggest common factor number .

Step-1: Prime Factorization of 19488

Prime factors of 19488 are 2, 3, 7, 29. Prime factorization of 19488 in exponential form is:

19488 = 2⁵ × 3¹ × 7¹ × 29¹

Step-2: Prime Factorization of 19504

Prime factors of 19504 are 2, 23, 53. Prime factorization of 19504 in exponential form is:

19504 = 2⁴ × 23¹ × 53¹

Step-3: Factors of 19488

List of positive integer factors of 19488 that divides 19488 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 84, 87, 96, 112, 116, 168, 174, 203, 224, 232, 336, 348, 406, 464, 609, 672, 696, 812, 928, 1218, 1392, 1624, 2436, 2784, 3248, 4872, 6496, 9744

Step-4: Factors of 19504

List of positive integer factors of 19504 that divides 19488 without a remainder.

1, 2, 4, 8, 16, 23, 46, 53, 92, 106, 184, 212, 368, 424, 848, 1219, 2438, 4876, 9752

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19488 and 19504. The biggest common factor number is the GCF number.
So the greatest common factor 19488 and 19504 is 16.

Also check out the Least Common Multiple of 19488 and 19504