What is the Greatest Common Factor of 27872 and 27884?

Greatest common factor (GCF) of 27872 and 27884 is 4.

GCF(27872,27884) = 4

We will now calculate the prime factors of 27872 and 27884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27872 and 27884.

How to find the GCF of 27872 and 27884?

We will first find the prime factorization of 27872 and 27884. After we will calculate the factors of 27872 and 27884 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 27884

Prime factors of 27884 are 2, 6971. Prime factorization of 27884 in exponential form is:

27884 = 2² × 6971¹

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 27884

List of positive integer factors of 27884 that divides 27872 without a remainder.

1, 2, 4, 6971, 13942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27872 and 27884. The biggest common factor number is the GCF number.
So the greatest common factor 27872 and 27884 is 4.

Also check out the Least Common Multiple of 27872 and 27884