What is the Greatest Common Factor of 5782 and 5800?

Greatest common factor (GCF) of 5782 and 5800 is 2.

GCF(5782,5800) = 2

We will now calculate the prime factors of 5782 and 5800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5782 and 5800.

How to find the GCF of 5782 and 5800?

We will first find the prime factorization of 5782 and 5800. After we will calculate the factors of 5782 and 5800 and find the biggest common factor number .

Step-1: Prime Factorization of 5782

Prime factors of 5782 are 2, 7, 59. Prime factorization of 5782 in exponential form is:

5782 = 2¹ × 7² × 59¹

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 5782

List of positive integer factors of 5782 that divides 5782 without a remainder.

1, 2, 7, 14, 49, 59, 98, 118, 413, 826, 2891

Step-4: Factors of 5800

List of positive integer factors of 5800 that divides 5782 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 5782 and 5800. The biggest common factor number is the GCF number.
So the greatest common factor 5782 and 5800 is 2.

Also check out the Least Common Multiple of 5782 and 5800