What is the Greatest Common Factor of 17678 and 17696?

Greatest common factor (GCF) of 17678 and 17696 is 2.

GCF(17678,17696) = 2

We will now calculate the prime factors of 17678 and 17696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17678 and 17696.

How to find the GCF of 17678 and 17696?

We will first find the prime factorization of 17678 and 17696. After we will calculate the factors of 17678 and 17696 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 17696

Prime factors of 17696 are 2, 7, 79. Prime factorization of 17696 in exponential form is:

17696 = 2⁵ × 7¹ × 79¹

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 17696

List of positive integer factors of 17696 that divides 17678 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 79, 112, 158, 224, 316, 553, 632, 1106, 1264, 2212, 2528, 4424, 8848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17678 and 17696. The biggest common factor number is the GCF number.
So the greatest common factor 17678 and 17696 is 2.

Also check out the Least Common Multiple of 17678 and 17696