What is the Greatest Common Factor of 17904 and 17919?

Greatest common factor (GCF) of 17904 and 17919 is 3.

GCF(17904,17919) = 3

We will now calculate the prime factors of 17904 and 17919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17904 and 17919.

How to find the GCF of 17904 and 17919?

We will first find the prime factorization of 17904 and 17919. After we will calculate the factors of 17904 and 17919 and find the biggest common factor number .

Step-1: Prime Factorization of 17904

Prime factors of 17904 are 2, 3, 373. Prime factorization of 17904 in exponential form is:

17904 = 2⁴ × 3¹ × 373¹

Step-2: Prime Factorization of 17919

Prime factors of 17919 are 3, 11, 181. Prime factorization of 17919 in exponential form is:

17919 = 3² × 11¹ × 181¹

Step-3: Factors of 17904

List of positive integer factors of 17904 that divides 17904 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 373, 746, 1119, 1492, 2238, 2984, 4476, 5968, 8952

Step-4: Factors of 17919

List of positive integer factors of 17919 that divides 17904 without a remainder.

1, 3, 9, 11, 33, 99, 181, 543, 1629, 1991, 5973

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17904 and 17919. The biggest common factor number is the GCF number.
So the greatest common factor 17904 and 17919 is 3.

Also check out the Least Common Multiple of 17904 and 17919