What is the Greatest Common Factor of 27872 and 27885?

Greatest common factor (GCF) of 27872 and 27885 is 13.

GCF(27872,27885) = 13

We will now calculate the prime factors of 27872 and 27885, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27872 and 27885.

How to find the GCF of 27872 and 27885?

We will first find the prime factorization of 27872 and 27885. After we will calculate the factors of 27872 and 27885 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 27885

Prime factors of 27885 are 3, 5, 11, 13. Prime factorization of 27885 in exponential form is:

27885 = 3¹ × 5¹ × 11¹ × 13²

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 27885

List of positive integer factors of 27885 that divides 27872 without a remainder.

1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 169, 195, 429, 507, 715, 845, 1859, 2145, 2535, 5577, 9295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27872 and 27885. The biggest common factor number is the GCF number.
So the greatest common factor 27872 and 27885 is 13.

Also check out the Least Common Multiple of 27872 and 27885