What is the Greatest Common Factor of 30791 and 30800?

Greatest common factor (GCF) of 30791 and 30800 is 1.

GCF(30791,30800) = 1

We will now calculate the prime factors of 30791 and 30800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30791 and 30800.

How to find the GCF of 30791 and 30800?

We will first find the prime factorization of 30791 and 30800. After we will calculate the factors of 30791 and 30800 and find the biggest common factor number .

Step-1: Prime Factorization of 30791

Prime factors of 30791 are 41, 751. Prime factorization of 30791 in exponential form is:

30791 = 41¹ × 751¹

Step-2: Prime Factorization of 30800

Prime factors of 30800 are 2, 5, 7, 11. Prime factorization of 30800 in exponential form is:

30800 = 2⁴ × 5² × 7¹ × 11¹

Step-3: Factors of 30791

List of positive integer factors of 30791 that divides 30791 without a remainder.

1, 41, 751

Step-4: Factors of 30800

List of positive integer factors of 30800 that divides 30791 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 175, 176, 200, 220, 275, 280, 308, 350, 385, 400, 440, 550, 560, 616, 700, 770, 880, 1100, 1232, 1400, 1540, 1925, 2200, 2800, 3080, 3850, 4400, 6160, 7700, 15400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30791 and 30800. The biggest common factor number is the GCF number.
So the greatest common factor 30791 and 30800 is 1.

Also check out the Least Common Multiple of 30791 and 30800