What is the Greatest Common Factor of 17914 and 17927?

Greatest common factor (GCF) of 17914 and 17927 is 13.

GCF(17914,17927) = 13

We will now calculate the prime factors of 17914 and 17927, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17927.

How to find the GCF of 17914 and 17927?

We will first find the prime factorization of 17914 and 17927. After we will calculate the factors of 17914 and 17927 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 17927

Prime factors of 17927 are 7, 13, 197. Prime factorization of 17927 in exponential form is:

17927 = 7¹ × 13¹ × 197¹

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 17927

List of positive integer factors of 17927 that divides 17914 without a remainder.

1, 7, 13, 91, 197, 1379, 2561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17927. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17927 is 13.

Also check out the Least Common Multiple of 17914 and 17927