What is the Greatest Common Factor of 19504 and 19520?

Greatest common factor (GCF) of 19504 and 19520 is 16.

GCF(19504,19520) = 16

We will now calculate the prime factors of 19504 and 19520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19504 and 19520.

How to find the GCF of 19504 and 19520?

We will first find the prime factorization of 19504 and 19520. After we will calculate the factors of 19504 and 19520 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 19520

Prime factors of 19520 are 2, 5, 61. Prime factorization of 19520 in exponential form is:

19520 = 2⁶ × 5¹ × 61¹

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 19520

List of positive integer factors of 19520 that divides 19504 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 61, 64, 80, 122, 160, 244, 305, 320, 488, 610, 976, 1220, 1952, 2440, 3904, 4880, 9760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19504 and 19520. The biggest common factor number is the GCF number.
So the greatest common factor 19504 and 19520 is 16.

Also check out the Least Common Multiple of 19504 and 19520