What is the Greatest Common Factor of 4575 and 4590?

Greatest common factor (GCF) of 4575 and 4590 is 15.

GCF(4575,4590) = 15

We will now calculate the prime factors of 4575 and 4590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4575 and 4590.

How to find the GCF of 4575 and 4590?

We will first find the prime factorization of 4575 and 4590. After we will calculate the factors of 4575 and 4590 and find the biggest common factor number .

Step-1: Prime Factorization of 4575

Prime factors of 4575 are 3, 5, 61. Prime factorization of 4575 in exponential form is:

4575 = 3¹ × 5² × 61¹

Step-2: Prime Factorization of 4590

Prime factors of 4590 are 2, 3, 5, 17. Prime factorization of 4590 in exponential form is:

4590 = 2¹ × 3³ × 5¹ × 17¹

Step-3: Factors of 4575

List of positive integer factors of 4575 that divides 4575 without a remainder.

1, 3, 5, 15, 25, 61, 75, 183, 305, 915, 1525

Step-4: Factors of 4590

List of positive integer factors of 4590 that divides 4575 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54, 85, 90, 102, 135, 153, 170, 255, 270, 306, 459, 510, 765, 918, 1530, 2295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4575 and 4590. The biggest common factor number is the GCF number.
So the greatest common factor 4575 and 4590 is 15.

Also check out the Least Common Multiple of 4575 and 4590