What is the Greatest Common Factor of 19890 and 19904?

Greatest common factor (GCF) of 19890 and 19904 is 2.

GCF(19890,19904) = 2

We will now calculate the prime factors of 19890 and 19904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19890 and 19904.

How to find the GCF of 19890 and 19904?

We will first find the prime factorization of 19890 and 19904. After we will calculate the factors of 19890 and 19904 and find the biggest common factor number .

Step-1: Prime Factorization of 19890

Prime factors of 19890 are 2, 3, 5, 13, 17. Prime factorization of 19890 in exponential form is:

19890 = 2¹ × 3² × 5¹ × 13¹ × 17¹

Step-2: Prime Factorization of 19904

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

19904 = 2⁶ × 311¹

Step-3: Factors of 19890

List of positive integer factors of 19890 that divides 19890 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 17, 18, 26, 30, 34, 39, 45, 51, 65, 78, 85, 90, 102, 117, 130, 153, 170, 195, 221, 234, 255, 306, 390, 442, 510, 585, 663, 765, 1105, 1170, 1326, 1530, 1989, 2210, 3315, 3978, 6630, 9945

Step-4: Factors of 19904

List of positive integer factors of 19904 that divides 19890 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19890 and 19904. The biggest common factor number is the GCF number.
So the greatest common factor 19890 and 19904 is 2.

Also check out the Least Common Multiple of 19890 and 19904