What is the Greatest Common Factor of 5872 and 5880?

Greatest common factor (GCF) of 5872 and 5880 is 8.

GCF(5872,5880) = 8

We will now calculate the prime factors of 5872 and 5880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5872 and 5880.

How to find the GCF of 5872 and 5880?

We will first find the prime factorization of 5872 and 5880. After we will calculate the factors of 5872 and 5880 and find the biggest common factor number .

Step-1: Prime Factorization of 5872

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

5872 = 2⁴ × 367¹

Step-2: Prime Factorization of 5880

Prime factors of 5880 are 2, 3, 5, 7. Prime factorization of 5880 in exponential form is:

5880 = 2³ × 3¹ × 5¹ × 7²

Step-3: Factors of 5872

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

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

Step-4: Factors of 5880

List of positive integer factors of 5880 that divides 5872 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, 392, 420, 490, 588, 735, 840, 980, 1176, 1470, 1960, 2940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5872 and 5880. The biggest common factor number is the GCF number.
So the greatest common factor 5872 and 5880 is 8.

Also check out the Least Common Multiple of 5872 and 5880