What is the Greatest Common Factor of 460 and 465?

Greatest common factor (GCF) of 460 and 465 is 5.

GCF(460,465) = 5

We will now calculate the prime factors of 460 and 465, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 460 and 465.

How to find the GCF of 460 and 465?

We will first find the prime factorization of 460 and 465. After we will calculate the factors of 460 and 465 and find the biggest common factor number .

Step-1: Prime Factorization of 460

Prime factors of 460 are 2, 5, 23. Prime factorization of 460 in exponential form is:

460 = 2² × 5¹ × 23¹

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 460

List of positive integer factors of 460 that divides 460 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230

Step-4: Factors of 465

List of positive integer factors of 465 that divides 460 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 460 and 465. The biggest common factor number is the GCF number.
So the greatest common factor 460 and 465 is 5.

Also check out the Least Common Multiple of 460 and 465