What is the Greatest Common Factor of 1008 and 1025?

Greatest common factor (GCF) of 1008 and 1025 is 1.

GCF(1008,1025) = 1

We will now calculate the prime factors of 1008 and 1025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1008 and 1025.

How to find the GCF of 1008 and 1025?

We will first find the prime factorization of 1008 and 1025. After we will calculate the factors of 1008 and 1025 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 1025

Prime factors of 1025 are 5, 41. Prime factorization of 1025 in exponential form is:

1025 = 5² × 41¹

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 1025

List of positive integer factors of 1025 that divides 1008 without a remainder.

1, 5, 25, 41, 205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1008 and 1025. The biggest common factor number is the GCF number.
So the greatest common factor 1008 and 1025 is 1.

Also check out the Least Common Multiple of 1008 and 1025