What is the Greatest Common Factor of 21573 and 21585?

Greatest common factor (GCF) of 21573 and 21585 is 3.

GCF(21573,21585) = 3

We will now calculate the prime factors of 21573 and 21585, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21573 and 21585.

How to find the GCF of 21573 and 21585?

We will first find the prime factorization of 21573 and 21585. After we will calculate the factors of 21573 and 21585 and find the biggest common factor number .

Step-1: Prime Factorization of 21573

Prime factors of 21573 are 3, 17, 47. Prime factorization of 21573 in exponential form is:

21573 = 3³ × 17¹ × 47¹

Step-2: Prime Factorization of 21585

Prime factors of 21585 are 3, 5, 1439. Prime factorization of 21585 in exponential form is:

21585 = 3¹ × 5¹ × 1439¹

Step-3: Factors of 21573

List of positive integer factors of 21573 that divides 21573 without a remainder.

1, 3, 9, 17, 27, 47, 51, 141, 153, 423, 459, 799, 1269, 2397, 7191

Step-4: Factors of 21585

List of positive integer factors of 21585 that divides 21573 without a remainder.

1, 3, 5, 15, 1439, 4317, 7195

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21573 and 21585. The biggest common factor number is the GCF number.
So the greatest common factor 21573 and 21585 is 3.

Also check out the Least Common Multiple of 21573 and 21585