What is the Greatest Common Factor of 30800 and 30814?

Greatest common factor (GCF) of 30800 and 30814 is 14.

GCF(30800,30814) = 14

We will now calculate the prime factors of 30800 and 30814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30800 and 30814.

How to find the GCF of 30800 and 30814?

We will first find the prime factorization of 30800 and 30814. After we will calculate the factors of 30800 and 30814 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30814

Prime factors of 30814 are 2, 7, 31, 71. Prime factorization of 30814 in exponential form is:

30814 = 2¹ × 7¹ × 31¹ × 71¹

Step-3: Factors of 30800

List of positive integer factors of 30800 that divides 30800 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

Step-4: Factors of 30814

List of positive integer factors of 30814 that divides 30800 without a remainder.

1, 2, 7, 14, 31, 62, 71, 142, 217, 434, 497, 994, 2201, 4402, 15407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30800 and 30814. The biggest common factor number is the GCF number.
So the greatest common factor 30800 and 30814 is 14.

Also check out the Least Common Multiple of 30800 and 30814