What is the Greatest Common Factor of 17678 and 17690?

Greatest common factor (GCF) of 17678 and 17690 is 2.

GCF(17678,17690) = 2

We will now calculate the prime factors of 17678 and 17690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17678 and 17690.

How to find the GCF of 17678 and 17690?

We will first find the prime factorization of 17678 and 17690. After we will calculate the factors of 17678 and 17690 and find the biggest common factor number .

Step-1: Prime Factorization of 17678

Prime factors of 17678 are 2, 8839. Prime factorization of 17678 in exponential form is:

17678 = 2¹ × 8839¹

Step-2: Prime Factorization of 17690

Prime factors of 17690 are 2, 5, 29, 61. Prime factorization of 17690 in exponential form is:

17690 = 2¹ × 5¹ × 29¹ × 61¹

Step-3: Factors of 17678

List of positive integer factors of 17678 that divides 17678 without a remainder.

1, 2, 8839

Step-4: Factors of 17690

List of positive integer factors of 17690 that divides 17678 without a remainder.

1, 2, 5, 10, 29, 58, 61, 122, 145, 290, 305, 610, 1769, 3538, 8845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17678 and 17690. The biggest common factor number is the GCF number.
So the greatest common factor 17678 and 17690 is 2.

Also check out the Least Common Multiple of 17678 and 17690