What is the Greatest Common Factor of 48 and 448?

Greatest common factor (GCF) of 48 and 448 is 16.

GCF(48,448) = 16

We will now calculate the prime factors of 48 and 448, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48 and 448.

How to find the GCF of 48 and 448?

We will first find the prime factorization of 48 and 448. After we will calculate the factors of 48 and 448 and find the biggest common factor number .

Step-1: Prime Factorization of 48

Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:

48 = 2⁴ × 3¹

Step-2: Prime Factorization of 448

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

448 = 2⁶ × 7¹

Step-3: Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24

Step-4: Factors of 448

List of positive integer factors of 448 that divides 48 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48 and 448. The biggest common factor number is the GCF number.
So the greatest common factor 48 and 448 is 16.

Also check out the Least Common Multiple of 48 and 448