What is the Greatest Common Factor of 780 and 789?

Greatest common factor (GCF) of 780 and 789 is 3.

GCF(780,789) = 3

We will now calculate the prime factors of 780 and 789, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 780 and 789.

How to find the GCF of 780 and 789?

We will first find the prime factorization of 780 and 789. After we will calculate the factors of 780 and 789 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 789

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

789 = 3¹ × 263¹

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 789

List of positive integer factors of 789 that divides 780 without a remainder.

1, 3, 263

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 780 and 789. The biggest common factor number is the GCF number.
So the greatest common factor 780 and 789 is 3.

Also check out the Least Common Multiple of 780 and 789