What is the Greatest Common Factor of 789 and 800?

Greatest common factor (GCF) of 789 and 800 is 1.

GCF(789,800) = 1

We will now calculate the prime factors of 789 and 800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 789 and 800.

How to find the GCF of 789 and 800?

We will first find the prime factorization of 789 and 800. After we will calculate the factors of 789 and 800 and find the biggest common factor number .

Step-1: Prime Factorization of 789

Prime factors of 789 are 3, 263. Prime factorization of 789 in exponential form is:

789 = 3¹ × 263¹

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 789

List of positive integer factors of 789 that divides 789 without a remainder.

1, 3, 263

Step-4: Factors of 800

List of positive integer factors of 800 that divides 789 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 789 and 800. The biggest common factor number is the GCF number.
So the greatest common factor 789 and 800 is 1.

Also check out the Least Common Multiple of 789 and 800