What is the Greatest Common Factor of 464 and 480?

Greatest common factor (GCF) of 464 and 480 is 16.

GCF(464,480) = 16

We will now calculate the prime factors of 464 and 480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 464 and 480.

How to find the GCF of 464 and 480?

We will first find the prime factorization of 464 and 480. After we will calculate the factors of 464 and 480 and find the biggest common factor number .

Step-1: Prime Factorization of 464

Prime factors of 464 are 2, 29. Prime factorization of 464 in exponential form is:

464 = 2⁴ × 29¹

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 464

List of positive integer factors of 464 that divides 464 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232

Step-4: Factors of 480

List of positive integer factors of 480 that divides 464 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 464 and 480. The biggest common factor number is the GCF number.
So the greatest common factor 464 and 480 is 16.

Also check out the Least Common Multiple of 464 and 480