What is the Greatest Common Factor of 27678 and 27696?

Greatest common factor (GCF) of 27678 and 27696 is 6.

GCF(27678,27696) = 6

We will now calculate the prime factors of 27678 and 27696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27678 and 27696.

How to find the GCF of 27678 and 27696?

We will first find the prime factorization of 27678 and 27696. After we will calculate the factors of 27678 and 27696 and find the biggest common factor number .

Step-1: Prime Factorization of 27678

Prime factors of 27678 are 2, 3, 7, 659. Prime factorization of 27678 in exponential form is:

27678 = 2¹ × 3¹ × 7¹ × 659¹

Step-2: Prime Factorization of 27696

Prime factors of 27696 are 2, 3, 577. Prime factorization of 27696 in exponential form is:

27696 = 2⁴ × 3¹ × 577¹

Step-3: Factors of 27678

List of positive integer factors of 27678 that divides 27678 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 659, 1318, 1977, 3954, 4613, 9226, 13839

Step-4: Factors of 27696

List of positive integer factors of 27696 that divides 27678 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 577, 1154, 1731, 2308, 3462, 4616, 6924, 9232, 13848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27678 and 27696. The biggest common factor number is the GCF number.
So the greatest common factor 27678 and 27696 is 6.

Also check out the Least Common Multiple of 27678 and 27696