What is the Greatest Common Factor of 17904 and 17914?

Greatest common factor (GCF) of 17904 and 17914 is 2.

GCF(17904,17914) = 2

We will now calculate the prime factors of 17904 and 17914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17904 and 17914.

How to find the GCF of 17904 and 17914?

We will first find the prime factorization of 17904 and 17914. After we will calculate the factors of 17904 and 17914 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 17914

Prime factors of 17914 are 2, 13, 53. Prime factorization of 17914 in exponential form is:

17914 = 2¹ × 13² × 53¹

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 17914

List of positive integer factors of 17914 that divides 17904 without a remainder.

1, 2, 13, 26, 53, 106, 169, 338, 689, 1378, 8957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17904 and 17914. The biggest common factor number is the GCF number.
So the greatest common factor 17904 and 17914 is 2.

Also check out the Least Common Multiple of 17904 and 17914