What is the Greatest Common Factor of 27696 and 27712?

Greatest common factor (GCF) of 27696 and 27712 is 16.

GCF(27696,27712) = 16

We will now calculate the prime factors of 27696 and 27712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27696 and 27712.

How to find the GCF of 27696 and 27712?

We will first find the prime factorization of 27696 and 27712. After we will calculate the factors of 27696 and 27712 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 27712

Prime factors of 27712 are 2, 433. Prime factorization of 27712 in exponential form is:

27712 = 2⁶ × 433¹

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 27712

List of positive integer factors of 27712 that divides 27696 without a remainder.

1, 2, 4, 8, 16, 32, 64, 433, 866, 1732, 3464, 6928, 13856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27696 and 27712. The biggest common factor number is the GCF number.
So the greatest common factor 27696 and 27712 is 16.

Also check out the Least Common Multiple of 27696 and 27712