What is the Greatest Common Factor of 10575 and 10580?

Greatest common factor (GCF) of 10575 and 10580 is 5.

GCF(10575,10580) = 5

We will now calculate the prime factors of 10575 and 10580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10575 and 10580.

How to find the GCF of 10575 and 10580?

We will first find the prime factorization of 10575 and 10580. After we will calculate the factors of 10575 and 10580 and find the biggest common factor number .

Step-1: Prime Factorization of 10575

Prime factors of 10575 are 3, 5, 47. Prime factorization of 10575 in exponential form is:

10575 = 3² × 5² × 47¹

Step-2: 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-3: Factors of 10575

List of positive integer factors of 10575 that divides 10575 without a remainder.

1, 3, 5, 9, 15, 25, 45, 47, 75, 141, 225, 235, 423, 705, 1175, 2115, 3525

Step-4: Factors of 10580

List of positive integer factors of 10580 that divides 10575 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10575 and 10580. The biggest common factor number is the GCF number.
So the greatest common factor 10575 and 10580 is 5.

Also check out the Least Common Multiple of 10575 and 10580