What is the Greatest Common Factor of 4800 and 4814?

Greatest common factor (GCF) of 4800 and 4814 is 2.

GCF(4800,4814) = 2

We will now calculate the prime factors of 4800 and 4814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4800 and 4814.

How to find the GCF of 4800 and 4814?

We will first find the prime factorization of 4800 and 4814. After we will calculate the factors of 4800 and 4814 and find the biggest common factor number .

Step-1: Prime Factorization of 4800

Prime factors of 4800 are 2, 3, 5. Prime factorization of 4800 in exponential form is:

4800 = 2⁶ × 3¹ × 5²

Step-2: Prime Factorization of 4814

Prime factors of 4814 are 2, 29, 83. Prime factorization of 4814 in exponential form is:

4814 = 2¹ × 29¹ × 83¹

Step-3: Factors of 4800

List of positive integer factors of 4800 that divides 4800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800, 960, 1200, 1600, 2400

Step-4: Factors of 4814

List of positive integer factors of 4814 that divides 4800 without a remainder.

1, 2, 29, 58, 83, 166, 2407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4800 and 4814. The biggest common factor number is the GCF number.
So the greatest common factor 4800 and 4814 is 2.

Also check out the Least Common Multiple of 4800 and 4814