What is the Greatest Common Factor of 5678 and 5696?

Greatest common factor (GCF) of 5678 and 5696 is 2.

GCF(5678,5696) = 2

We will now calculate the prime factors of 5678 and 5696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5678 and 5696.

How to find the GCF of 5678 and 5696?

We will first find the prime factorization of 5678 and 5696. After we will calculate the factors of 5678 and 5696 and find the biggest common factor number .

Step-1: Prime Factorization of 5678

Prime factors of 5678 are 2, 17, 167. Prime factorization of 5678 in exponential form is:

5678 = 2¹ × 17¹ × 167¹

Step-2: Prime Factorization of 5696

Prime factors of 5696 are 2, 89. Prime factorization of 5696 in exponential form is:

5696 = 2⁶ × 89¹

Step-3: Factors of 5678

List of positive integer factors of 5678 that divides 5678 without a remainder.

1, 2, 17, 34, 167, 334, 2839

Step-4: Factors of 5696

List of positive integer factors of 5696 that divides 5678 without a remainder.

1, 2, 4, 8, 16, 32, 64, 89, 178, 356, 712, 1424, 2848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5678 and 5696. The biggest common factor number is the GCF number.
So the greatest common factor 5678 and 5696 is 2.

Also check out the Least Common Multiple of 5678 and 5696