What is the Greatest Common Factor of 462 and 480?

Greatest common factor (GCF) of 462 and 480 is 6.

GCF(462,480) = 6

We will now calculate the prime factors of 462 and 480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 462 and 480.

How to find the GCF of 462 and 480?

We will first find the prime factorization of 462 and 480. After we will calculate the factors of 462 and 480 and find the biggest common factor number .

Step-1: Prime Factorization of 462

Prime factors of 462 are 2, 3, 7, 11. Prime factorization of 462 in exponential form is:

462 = 2¹ × 3¹ × 7¹ × 11¹

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 462

List of positive integer factors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231

Step-4: Factors of 480

List of positive integer factors of 480 that divides 462 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 462 and 480. The biggest common factor number is the GCF number.
So the greatest common factor 462 and 480 is 6.

Also check out the Least Common Multiple of 462 and 480