What is the Greatest Common Factor of 27854 and 27872?

Greatest common factor (GCF) of 27854 and 27872 is 2.

GCF(27854,27872) = 2

We will now calculate the prime factors of 27854 and 27872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27854 and 27872.

How to find the GCF of 27854 and 27872?

We will first find the prime factorization of 27854 and 27872. After we will calculate the factors of 27854 and 27872 and find the biggest common factor number .

Step-1: Prime Factorization of 27854

Prime factors of 27854 are 2, 19, 733. Prime factorization of 27854 in exponential form is:

27854 = 2¹ × 19¹ × 733¹

Step-2: Prime Factorization of 27872

Prime factors of 27872 are 2, 13, 67. Prime factorization of 27872 in exponential form is:

27872 = 2⁵ × 13¹ × 67¹

Step-3: Factors of 27854

List of positive integer factors of 27854 that divides 27854 without a remainder.

1, 2, 19, 38, 733, 1466, 13927

Step-4: Factors of 27872

List of positive integer factors of 27872 that divides 27854 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 67, 104, 134, 208, 268, 416, 536, 871, 1072, 1742, 2144, 3484, 6968, 13936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27854 and 27872. The biggest common factor number is the GCF number.
So the greatest common factor 27854 and 27872 is 2.

Also check out the Least Common Multiple of 27854 and 27872