What is the Greatest Common Factor of 1008 and 1024?

Greatest common factor (GCF) of 1008 and 1024 is 16.

GCF(1008,1024) = 16

We will now calculate the prime factors of 1008 and 1024, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1008 and 1024.

How to find the GCF of 1008 and 1024?

We will first find the prime factorization of 1008 and 1024. After we will calculate the factors of 1008 and 1024 and find the biggest common factor number .

Step-1: Prime Factorization of 1008

Prime factors of 1008 are 2, 3, 7. Prime factorization of 1008 in exponential form is:

1008 = 2⁴ × 3² × 7¹

Step-2: Prime Factorization of 1024

Prime factors of 1024 are 2. Prime factorization of 1024 in exponential form is:

1024 = 2¹⁰

Step-3: Factors of 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504

Step-4: Factors of 1024

List of positive integer factors of 1024 that divides 1008 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1008 and 1024. The biggest common factor number is the GCF number.
So the greatest common factor 1008 and 1024 is 16.

Also check out the Least Common Multiple of 1008 and 1024