What is the Greatest Common Factor of 17714 and 17731?

Greatest common factor (GCF) of 17714 and 17731 is 17.

GCF(17714,17731) = 17

We will now calculate the prime factors of 17714 and 17731, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17714 and 17731.

How to find the GCF of 17714 and 17731?

We will first find the prime factorization of 17714 and 17731. After we will calculate the factors of 17714 and 17731 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17731

Prime factors of 17731 are 7, 17, 149. Prime factorization of 17731 in exponential form is:

17731 = 7¹ × 17¹ × 149¹

Step-3: Factors of 17714

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

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

Step-4: Factors of 17731

List of positive integer factors of 17731 that divides 17714 without a remainder.

1, 7, 17, 119, 149, 1043, 2533

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17714 and 17731. The biggest common factor number is the GCF number.
So the greatest common factor 17714 and 17731 is 17.

Also check out the Least Common Multiple of 17714 and 17731