What is the Greatest Common Factor of 10580 and 10585?

Greatest common factor (GCF) of 10580 and 10585 is 5.

GCF(10580,10585) = 5

We will now calculate the prime factors of 10580 and 10585, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10580 and 10585.

How to find the GCF of 10580 and 10585?

We will first find the prime factorization of 10580 and 10585. After we will calculate the factors of 10580 and 10585 and find the biggest common factor number .

Step-1: Prime Factorization of 10580

Prime factors of 10580 are 2, 5, 23. Prime factorization of 10580 in exponential form is:

10580 = 2² × 5¹ × 23²

Step-2: Prime Factorization of 10585

Prime factors of 10585 are 5, 29, 73. Prime factorization of 10585 in exponential form is:

10585 = 5¹ × 29¹ × 73¹

Step-3: Factors of 10580

List of positive integer factors of 10580 that divides 10580 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460, 529, 1058, 2116, 2645, 5290

Step-4: Factors of 10585

List of positive integer factors of 10585 that divides 10580 without a remainder.

1, 5, 29, 73, 145, 365, 2117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10580 and 10585. The biggest common factor number is the GCF number.
So the greatest common factor 10580 and 10585 is 5.

Also check out the Least Common Multiple of 10580 and 10585