What is the Greatest Common Factor of 448 and 456?

Greatest common factor (GCF) of 448 and 456 is 8.

GCF(448,456) = 8

We will now calculate the prime factors of 448 and 456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 448 and 456.

How to find the GCF of 448 and 456?

We will first find the prime factorization of 448 and 456. After we will calculate the factors of 448 and 456 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 456

Prime factors of 456 are 2, 3, 19. Prime factorization of 456 in exponential form is:

456 = 2³ × 3¹ × 19¹

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 456

List of positive integer factors of 456 that divides 448 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 448 and 456. The biggest common factor number is the GCF number.
So the greatest common factor 448 and 456 is 8.

Also check out the Least Common Multiple of 448 and 456