What is the Greatest Common Factor of 448 and 462?

Greatest common factor (GCF) of 448 and 462 is 14.

GCF(448,462) = 14

We will now calculate the prime factors of 448 and 462, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 448 and 462.

How to find the GCF of 448 and 462?

We will first find the prime factorization of 448 and 462. After we will calculate the factors of 448 and 462 and find the biggest common factor number .

Step-1: Prime Factorization of 448

Prime factors of 448 are 2, 7. Prime factorization of 448 in exponential form is:

448 = 2⁶ × 7¹

Step-2: 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-3: Factors of 448

List of positive integer factors of 448 that divides 448 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224

Step-4: Factors of 462

List of positive integer factors of 462 that divides 448 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 448 and 462. The biggest common factor number is the GCF number.
So the greatest common factor 448 and 462 is 14.

Also check out the Least Common Multiple of 448 and 462