What is the Greatest Common Factor of 27696 and 27714?

Greatest common factor (GCF) of 27696 and 27714 is 6.

GCF(27696,27714) = 6

We will now calculate the prime factors of 27696 and 27714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27696 and 27714.

How to find the GCF of 27696 and 27714?

We will first find the prime factorization of 27696 and 27714. After we will calculate the factors of 27696 and 27714 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27714

Prime factors of 27714 are 2, 3, 31, 149. Prime factorization of 27714 in exponential form is:

27714 = 2¹ × 3¹ × 31¹ × 149¹

Step-3: Factors of 27696

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

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

Step-4: Factors of 27714

List of positive integer factors of 27714 that divides 27696 without a remainder.

1, 2, 3, 6, 31, 62, 93, 149, 186, 298, 447, 894, 4619, 9238, 13857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27696 and 27714. The biggest common factor number is the GCF number.
So the greatest common factor 27696 and 27714 is 6.

Also check out the Least Common Multiple of 27696 and 27714