What is the Greatest Common Factor of 17914 and 17934?

Greatest common factor (GCF) of 17914 and 17934 is 2.

GCF(17914,17934) = 2

We will now calculate the prime factors of 17914 and 17934, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17934.

How to find the GCF of 17914 and 17934?

We will first find the prime factorization of 17914 and 17934. After we will calculate the factors of 17914 and 17934 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 17934

Prime factors of 17934 are 2, 3, 7, 61. Prime factorization of 17934 in exponential form is:

17934 = 2¹ × 3¹ × 7² × 61¹

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 17934

List of positive integer factors of 17934 that divides 17914 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 61, 98, 122, 147, 183, 294, 366, 427, 854, 1281, 2562, 2989, 5978, 8967

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17934. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17934 is 2.

Also check out the Least Common Multiple of 17914 and 17934