What is the Greatest Common Factor of 27872 and 27878?

Greatest common factor (GCF) of 27872 and 27878 is 2.

GCF(27872,27878) = 2

We will now calculate the prime factors of 27872 and 27878, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27872 and 27878.

How to find the GCF of 27872 and 27878?

We will first find the prime factorization of 27872 and 27878. After we will calculate the factors of 27872 and 27878 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27878

Prime factors of 27878 are 2, 53, 263. Prime factorization of 27878 in exponential form is:

27878 = 2¹ × 53¹ × 263¹

Step-3: Factors of 27872

List of positive integer factors of 27872 that divides 27872 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

Step-4: Factors of 27878

List of positive integer factors of 27878 that divides 27872 without a remainder.

1, 2, 53, 106, 263, 526, 13939

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27872 and 27878. The biggest common factor number is the GCF number.
So the greatest common factor 27872 and 27878 is 2.

Also check out the Least Common Multiple of 27872 and 27878