What is the Greatest Common Factor of 17704 and 17714?

Greatest common factor (GCF) of 17704 and 17714 is 2.

GCF(17704,17714) = 2

We will now calculate the prime factors of 17704 and 17714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17704 and 17714.

How to find the GCF of 17704 and 17714?

We will first find the prime factorization of 17704 and 17714. After we will calculate the factors of 17704 and 17714 and find the biggest common factor number .

Step-1: Prime Factorization of 17704

Prime factors of 17704 are 2, 2213. Prime factorization of 17704 in exponential form is:

17704 = 2³ × 2213¹

Step-2: Prime Factorization of 17714

Prime factors of 17714 are 2, 17, 521. Prime factorization of 17714 in exponential form is:

17714 = 2¹ × 17¹ × 521¹

Step-3: Factors of 17704

List of positive integer factors of 17704 that divides 17704 without a remainder.

1, 2, 4, 8, 2213, 4426, 8852

Step-4: Factors of 17714

List of positive integer factors of 17714 that divides 17704 without a remainder.

1, 2, 17, 34, 521, 1042, 8857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17704 and 17714. The biggest common factor number is the GCF number.
So the greatest common factor 17704 and 17714 is 2.

Also check out the Least Common Multiple of 17704 and 17714