What is the Greatest Common Factor of 17914 and 17922?

Greatest common factor (GCF) of 17914 and 17922 is 2.

GCF(17914,17922) = 2

We will now calculate the prime factors of 17914 and 17922, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17922.

How to find the GCF of 17914 and 17922?

We will first find the prime factorization of 17914 and 17922. After we will calculate the factors of 17914 and 17922 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 17922

Prime factors of 17922 are 2, 3, 29, 103. Prime factorization of 17922 in exponential form is:

17922 = 2¹ × 3¹ × 29¹ × 103¹

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 17922

List of positive integer factors of 17922 that divides 17914 without a remainder.

1, 2, 3, 6, 29, 58, 87, 103, 174, 206, 309, 618, 2987, 5974, 8961

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17922. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17922 is 2.

Also check out the Least Common Multiple of 17914 and 17922