What is the Greatest Common Factor of 5785 and 5800?

Greatest common factor (GCF) of 5785 and 5800 is 5.

GCF(5785,5800) = 5

We will now calculate the prime factors of 5785 and 5800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5785 and 5800.

How to find the GCF of 5785 and 5800?

We will first find the prime factorization of 5785 and 5800. After we will calculate the factors of 5785 and 5800 and find the biggest common factor number .

Step-1: Prime Factorization of 5785

Prime factors of 5785 are 5, 13, 89. Prime factorization of 5785 in exponential form is:

5785 = 5¹ × 13¹ × 89¹

Step-2: Prime Factorization of 5800

Prime factors of 5800 are 2, 5, 29. Prime factorization of 5800 in exponential form is:

5800 = 2³ × 5² × 29¹

Step-3: Factors of 5785

List of positive integer factors of 5785 that divides 5785 without a remainder.

1, 5, 13, 65, 89, 445, 1157

Step-4: Factors of 5800

List of positive integer factors of 5800 that divides 5785 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 29, 40, 50, 58, 100, 116, 145, 200, 232, 290, 580, 725, 1160, 1450, 2900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5785 and 5800. The biggest common factor number is the GCF number.
So the greatest common factor 5785 and 5800 is 5.

Also check out the Least Common Multiple of 5785 and 5800