What is the Greatest Common Factor of 465 and 480?

Greatest common factor (GCF) of 465 and 480 is 15.

GCF(465,480) = 15

We will now calculate the prime factors of 465 and 480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 465 and 480.

How to find the GCF of 465 and 480?

We will first find the prime factorization of 465 and 480. After we will calculate the factors of 465 and 480 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 480

Prime factors of 480 are 2, 3, 5. Prime factorization of 480 in exponential form is:

480 = 2⁵ × 3¹ × 5¹

Step-3: Factors of 465

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

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

Step-4: Factors of 480

List of positive integer factors of 480 that divides 465 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 465 and 480. The biggest common factor number is the GCF number.
So the greatest common factor 465 and 480 is 15.

Also check out the Least Common Multiple of 465 and 480