What is the Greatest Common Factor of 17914 and 17931?

Greatest common factor (GCF) of 17914 and 17931 is 1.

GCF(17914,17931) = 1

We will now calculate the prime factors of 17914 and 17931, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17931.

How to find the GCF of 17914 and 17931?

We will first find the prime factorization of 17914 and 17931. After we will calculate the factors of 17914 and 17931 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 17931

Prime factors of 17931 are 3, 43, 139. Prime factorization of 17931 in exponential form is:

17931 = 3¹ × 43¹ × 139¹

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 17931

List of positive integer factors of 17931 that divides 17914 without a remainder.

1, 3, 43, 129, 139, 417, 5977

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17931. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17931 is 1.

Also check out the Least Common Multiple of 17914 and 17931