What is the Greatest Common Factor of 450 and 465?

Greatest common factor (GCF) of 450 and 465 is 15.

GCF(450,465) = 15

We will now calculate the prime factors of 450 and 465, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 450 and 465.

How to find the GCF of 450 and 465?

We will first find the prime factorization of 450 and 465. After we will calculate the factors of 450 and 465 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 465

Prime factors of 465 are 3, 5, 31. Prime factorization of 465 in exponential form is:

465 = 3¹ × 5¹ × 31¹

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 465

List of positive integer factors of 465 that divides 450 without a remainder.

1, 3, 5, 15, 31, 93, 155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 450 and 465. The biggest common factor number is the GCF number.
So the greatest common factor 450 and 465 is 15.

Also check out the Least Common Multiple of 450 and 465