What is the Greatest Common Factor of 17914 and 17928?

Greatest common factor (GCF) of 17914 and 17928 is 2.

GCF(17914,17928) = 2

We will now calculate the prime factors of 17914 and 17928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17928.

How to find the GCF of 17914 and 17928?

We will first find the prime factorization of 17914 and 17928. After we will calculate the factors of 17914 and 17928 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17928

Prime factors of 17928 are 2, 3, 83. Prime factorization of 17928 in exponential form is:

17928 = 2³ × 3³ × 83¹

Step-3: Factors of 17914

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

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

Step-4: Factors of 17928

List of positive integer factors of 17928 that divides 17914 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 83, 108, 166, 216, 249, 332, 498, 664, 747, 996, 1494, 1992, 2241, 2988, 4482, 5976, 8964

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17928. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17928 is 2.

Also check out the Least Common Multiple of 17914 and 17928