What is the Greatest Common Factor of 2784 and 2800?

Greatest common factor (GCF) of 2784 and 2800 is 16.

GCF(2784,2800) = 16

We will now calculate the prime factors of 2784 and 2800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2784 and 2800.

How to find the GCF of 2784 and 2800?

We will first find the prime factorization of 2784 and 2800. After we will calculate the factors of 2784 and 2800 and find the biggest common factor number .

Step-1: Prime Factorization of 2784

Prime factors of 2784 are 2, 3, 29. Prime factorization of 2784 in exponential form is:

2784 = 2⁵ × 3¹ × 29¹

Step-2: 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-3: Factors of 2784

List of positive integer factors of 2784 that divides 2784 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 32, 48, 58, 87, 96, 116, 174, 232, 348, 464, 696, 928, 1392

Step-4: Factors of 2800

List of positive integer factors of 2800 that divides 2784 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2784 and 2800. The biggest common factor number is the GCF number.
So the greatest common factor 2784 and 2800 is 16.

Also check out the Least Common Multiple of 2784 and 2800