What is the Greatest Common Factor of 2800 and 2805?

Greatest common factor (GCF) of 2800 and 2805 is 5.

GCF(2800,2805) = 5

We will now calculate the prime factors of 2800 and 2805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2800 and 2805.

How to find the GCF of 2800 and 2805?

We will first find the prime factorization of 2800 and 2805. After we will calculate the factors of 2800 and 2805 and find the biggest common factor number .

Step-1: Prime Factorization of 2800

Prime factors of 2800 are 2, 5, 7. Prime factorization of 2800 in exponential form is:

2800 = 2⁴ × 5² × 7¹

Step-2: Prime Factorization of 2805

Prime factors of 2805 are 3, 5, 11, 17. Prime factorization of 2805 in exponential form is:

2805 = 3¹ × 5¹ × 11¹ × 17¹

Step-3: Factors of 2800

List of positive integer factors of 2800 that divides 2800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400

Step-4: Factors of 2805

List of positive integer factors of 2805 that divides 2800 without a remainder.

1, 3, 5, 11, 15, 17, 33, 51, 55, 85, 165, 187, 255, 561, 935

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2800 and 2805. The biggest common factor number is the GCF number.
So the greatest common factor 2800 and 2805 is 5.

Also check out the Least Common Multiple of 2800 and 2805