What is the Greatest Common Factor of 128 and 144?

Greatest common factor (GCF) of 128 and 144 is 16.

GCF(128,144) = 16

We will now calculate the prime factors of 128 and 144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 128 and 144.

How to find the GCF of 128 and 144?

We will first find the prime factorization of 128 and 144. After we will calculate the factors of 128 and 144 and find the biggest common factor number .

Step-1: Prime Factorization of 128

Prime factors of 128 are 2. Prime factorization of 128 in exponential form is:

128 = 2⁷

Step-2: Prime Factorization of 144

Prime factors of 144 are 2, 3. Prime factorization of 144 in exponential form is:

144 = 2⁴ × 3²

Step-3: Factors of 128

List of positive integer factors of 128 that divides 128 without a remainder.

1, 2, 4, 8, 16, 32, 64

Step-4: Factors of 144

List of positive integer factors of 144 that divides 128 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 128 and 144. The biggest common factor number is the GCF number.
So the greatest common factor 128 and 144 is 16.

Also check out the Least Common Multiple of 128 and 144