What is the Greatest Common Factor of 1006 and 1025?

Greatest common factor (GCF) of 1006 and 1025 is 1.

GCF(1006,1025) = 1

We will now calculate the prime factors of 1006 and 1025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1006 and 1025.

How to find the GCF of 1006 and 1025?

We will first find the prime factorization of 1006 and 1025. After we will calculate the factors of 1006 and 1025 and find the biggest common factor number .

Step-1: Prime Factorization of 1006

Prime factors of 1006 are 2, 503. Prime factorization of 1006 in exponential form is:

1006 = 2¹ × 503¹

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 1006

List of positive integer factors of 1006 that divides 1006 without a remainder.

1, 2, 503

Step-4: Factors of 1025

List of positive integer factors of 1025 that divides 1006 without a remainder.

1, 5, 25, 41, 205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1006 and 1025. The biggest common factor number is the GCF number.
So the greatest common factor 1006 and 1025 is 1.

Also check out the Least Common Multiple of 1006 and 1025