What is the Greatest Common Factor of 30782 and 30800?

Greatest common factor (GCF) of 30782 and 30800 is 2.

GCF(30782,30800) = 2

We will now calculate the prime factors of 30782 and 30800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30782 and 30800.

How to find the GCF of 30782 and 30800?

We will first find the prime factorization of 30782 and 30800. After we will calculate the factors of 30782 and 30800 and find the biggest common factor number .

Step-1: Prime Factorization of 30782

Prime factors of 30782 are 2, 15391. Prime factorization of 30782 in exponential form is:

30782 = 2¹ × 15391¹

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 30782

List of positive integer factors of 30782 that divides 30782 without a remainder.

1, 2, 15391

Step-4: Factors of 30800

List of positive integer factors of 30800 that divides 30782 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 30782 and 30800. The biggest common factor number is the GCF number.
So the greatest common factor 30782 and 30800 is 2.

Also check out the Least Common Multiple of 30782 and 30800