What is the Greatest Common Factor of 480 and 493?

Greatest common factor (GCF) of 480 and 493 is 1.

GCF(480,493) = 1

We will now calculate the prime factors of 480 and 493, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 480 and 493.

How to find the GCF of 480 and 493?

We will first find the prime factorization of 480 and 493. After we will calculate the factors of 480 and 493 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 493

Prime factors of 493 are 17, 29. Prime factorization of 493 in exponential form is:

493 = 17¹ × 29¹

Step-3: Factors of 480

List of positive integer factors of 480 that divides 480 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

Step-4: Factors of 493

List of positive integer factors of 493 that divides 480 without a remainder.

1, 17, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 480 and 493. The biggest common factor number is the GCF number.
So the greatest common factor 480 and 493 is 1.

Also check out the Least Common Multiple of 480 and 493