What is the Greatest Common Factor of 450 and 459?

Greatest common factor (GCF) of 450 and 459 is 9.

GCF(450,459) = 9

We will now calculate the prime factors of 450 and 459, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 450 and 459.

How to find the GCF of 450 and 459?

We will first find the prime factorization of 450 and 459. After we will calculate the factors of 450 and 459 and find the biggest common factor number .

Step-1: Prime Factorization of 450

Prime factors of 450 are 2, 3, 5. Prime factorization of 450 in exponential form is:

450 = 2¹ × 3² × 5²

Step-2: Prime Factorization of 459

Prime factors of 459 are 3, 17. Prime factorization of 459 in exponential form is:

459 = 3³ × 17¹

Step-3: Factors of 450

List of positive integer factors of 450 that divides 450 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225

Step-4: Factors of 459

List of positive integer factors of 459 that divides 450 without a remainder.

1, 3, 9, 17, 27, 51, 153

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 450 and 459. The biggest common factor number is the GCF number.
So the greatest common factor 450 and 459 is 9.

Also check out the Least Common Multiple of 450 and 459