What is the Greatest Common Factor of 780 and 800?

Greatest common factor (GCF) of 780 and 800 is 20.

GCF(780,800) = 20

We will now calculate the prime factors of 780 and 800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 780 and 800.

How to find the GCF of 780 and 800?

We will first find the prime factorization of 780 and 800. After we will calculate the factors of 780 and 800 and find the biggest common factor number .

Step-1: Prime Factorization of 780

Prime factors of 780 are 2, 3, 5, 13. Prime factorization of 780 in exponential form is:

780 = 2² × 3¹ × 5¹ × 13¹

Step-2: Prime Factorization of 800

Prime factors of 800 are 2, 5. Prime factorization of 800 in exponential form is:

800 = 2⁵ × 5²

Step-3: Factors of 780

List of positive integer factors of 780 that divides 780 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390

Step-4: Factors of 800

List of positive integer factors of 800 that divides 780 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 780 and 800. The biggest common factor number is the GCF number.
So the greatest common factor 780 and 800 is 20.

Also check out the Least Common Multiple of 780 and 800