What is the Greatest Common Factor of 19504 and 19516?

Greatest common factor (GCF) of 19504 and 19516 is 4.

GCF(19504,19516) = 4

We will now calculate the prime factors of 19504 and 19516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19504 and 19516.

How to find the GCF of 19504 and 19516?

We will first find the prime factorization of 19504 and 19516. After we will calculate the factors of 19504 and 19516 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19516

Prime factors of 19516 are 2, 7, 17, 41. Prime factorization of 19516 in exponential form is:

19516 = 2² × 7¹ × 17¹ × 41¹

Step-3: Factors of 19504

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

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

Step-4: Factors of 19516

List of positive integer factors of 19516 that divides 19504 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 41, 68, 82, 119, 164, 238, 287, 476, 574, 697, 1148, 1394, 2788, 4879, 9758

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19504 and 19516. The biggest common factor number is the GCF number.
So the greatest common factor 19504 and 19516 is 4.

Also check out the Least Common Multiple of 19504 and 19516