What is the Greatest Common Factor of 19904 and 19920?

Greatest common factor (GCF) of 19904 and 19920 is 16.

GCF(19904,19920) = 16

We will now calculate the prime factors of 19904 and 19920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19904 and 19920.

How to find the GCF of 19904 and 19920?

We will first find the prime factorization of 19904 and 19920. After we will calculate the factors of 19904 and 19920 and find the biggest common factor number .

Step-1: Prime Factorization of 19904

Prime factors of 19904 are 2, 311. Prime factorization of 19904 in exponential form is:

19904 = 2⁶ × 311¹

Step-2: Prime Factorization of 19920

Prime factors of 19920 are 2, 3, 5, 83. Prime factorization of 19920 in exponential form is:

19920 = 2⁴ × 3¹ × 5¹ × 83¹

Step-3: Factors of 19904

List of positive integer factors of 19904 that divides 19904 without a remainder.

1, 2, 4, 8, 16, 32, 64, 311, 622, 1244, 2488, 4976, 9952

Step-4: Factors of 19920

List of positive integer factors of 19920 that divides 19904 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 83, 120, 166, 240, 249, 332, 415, 498, 664, 830, 996, 1245, 1328, 1660, 1992, 2490, 3320, 3984, 4980, 6640, 9960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19904 and 19920. The biggest common factor number is the GCF number.
So the greatest common factor 19904 and 19920 is 16.

Also check out the Least Common Multiple of 19904 and 19920