What is the Greatest Common Factor of 19875 and 19890?

Greatest common factor (GCF) of 19875 and 19890 is 15.

GCF(19875,19890) = 15

We will now calculate the prime factors of 19875 and 19890, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19875 and 19890.

How to find the GCF of 19875 and 19890?

We will first find the prime factorization of 19875 and 19890. After we will calculate the factors of 19875 and 19890 and find the biggest common factor number .

Step-1: Prime Factorization of 19875

Prime factors of 19875 are 3, 5, 53. Prime factorization of 19875 in exponential form is:

19875 = 3¹ × 5³ × 53¹

Step-2: 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-3: Factors of 19875

List of positive integer factors of 19875 that divides 19875 without a remainder.

1, 3, 5, 15, 25, 53, 75, 125, 159, 265, 375, 795, 1325, 3975, 6625

Step-4: Factors of 19890

List of positive integer factors of 19890 that divides 19875 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19875 and 19890. The biggest common factor number is the GCF number.
So the greatest common factor 19875 and 19890 is 15.

Also check out the Least Common Multiple of 19875 and 19890