What is the Greatest Common Factor of 4785 and 4800?

Greatest common factor (GCF) of 4785 and 4800 is 15.

GCF(4785,4800) = 15

We will now calculate the prime factors of 4785 and 4800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4785 and 4800.

How to find the GCF of 4785 and 4800?

We will first find the prime factorization of 4785 and 4800. After we will calculate the factors of 4785 and 4800 and find the biggest common factor number .

Step-1: Prime Factorization of 4785

Prime factors of 4785 are 3, 5, 11, 29. Prime factorization of 4785 in exponential form is:

4785 = 3¹ × 5¹ × 11¹ × 29¹

Step-2: 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-3: Factors of 4785

List of positive integer factors of 4785 that divides 4785 without a remainder.

1, 3, 5, 11, 15, 29, 33, 55, 87, 145, 165, 319, 435, 957, 1595

Step-4: Factors of 4800

List of positive integer factors of 4800 that divides 4785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4785 and 4800. The biggest common factor number is the GCF number.
So the greatest common factor 4785 and 4800 is 15.

Also check out the Least Common Multiple of 4785 and 4800