What is the Greatest Common Factor of 2800 and 2812?

Greatest common factor (GCF) of 2800 and 2812 is 4.

GCF(2800,2812) = 4

We will now calculate the prime factors of 2800 and 2812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2800 and 2812.

How to find the GCF of 2800 and 2812?

We will first find the prime factorization of 2800 and 2812. After we will calculate the factors of 2800 and 2812 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 2812

Prime factors of 2812 are 2, 19, 37. Prime factorization of 2812 in exponential form is:

2812 = 2² × 19¹ × 37¹

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 2812

List of positive integer factors of 2812 that divides 2800 without a remainder.

1, 2, 4, 19, 37, 38, 74, 76, 148, 703, 1406

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2800 and 2812. The biggest common factor number is the GCF number.
So the greatest common factor 2800 and 2812 is 4.

Also check out the Least Common Multiple of 2800 and 2812