What is the Greatest Common Factor of 2780 and 2800?

Greatest common factor (GCF) of 2780 and 2800 is 20.

GCF(2780,2800) = 20

We will now calculate the prime factors of 2780 and 2800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2780 and 2800.

How to find the GCF of 2780 and 2800?

We will first find the prime factorization of 2780 and 2800. After we will calculate the factors of 2780 and 2800 and find the biggest common factor number .

Step-1: Prime Factorization of 2780

Prime factors of 2780 are 2, 5, 139. Prime factorization of 2780 in exponential form is:

2780 = 2² × 5¹ × 139¹

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 2780

List of positive integer factors of 2780 that divides 2780 without a remainder.

1, 2, 4, 5, 10, 20, 139, 278, 556, 695, 1390

Step-4: Factors of 2800

List of positive integer factors of 2800 that divides 2780 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 2780 and 2800. The biggest common factor number is the GCF number.
So the greatest common factor 2780 and 2800 is 20.

Also check out the Least Common Multiple of 2780 and 2800