What is the Greatest Common Factor of 5854 and 5872?

Greatest common factor (GCF) of 5854 and 5872 is 2.

GCF(5854,5872) = 2

We will now calculate the prime factors of 5854 and 5872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5854 and 5872.

How to find the GCF of 5854 and 5872?

We will first find the prime factorization of 5854 and 5872. After we will calculate the factors of 5854 and 5872 and find the biggest common factor number .

Step-1: Prime Factorization of 5854

Prime factors of 5854 are 2, 2927. Prime factorization of 5854 in exponential form is:

5854 = 2¹ × 2927¹

Step-2: Prime Factorization of 5872

Prime factors of 5872 are 2, 367. Prime factorization of 5872 in exponential form is:

5872 = 2⁴ × 367¹

Step-3: Factors of 5854

List of positive integer factors of 5854 that divides 5854 without a remainder.

1, 2, 2927

Step-4: Factors of 5872

List of positive integer factors of 5872 that divides 5854 without a remainder.

1, 2, 4, 8, 16, 367, 734, 1468, 2936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5854 and 5872. The biggest common factor number is the GCF number.
So the greatest common factor 5854 and 5872 is 2.

Also check out the Least Common Multiple of 5854 and 5872