What is the Greatest Common Factor of 2005 and 2021?

Greatest common factor (GCF) of 2005 and 2021 is 1.

GCF(2005,2021) = 1

We will now calculate the prime factors of 2005 and 2021, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2005 and 2021.

How to find the GCF of 2005 and 2021?

We will first find the prime factorization of 2005 and 2021. After we will calculate the factors of 2005 and 2021 and find the biggest common factor number .

Step-1: Prime Factorization of 2005

Prime factors of 2005 are 5, 401. Prime factorization of 2005 in exponential form is:

2005 = 5¹ × 401¹

Step-2: Prime Factorization of 2021

Prime factors of 2021 are 43, 47. Prime factorization of 2021 in exponential form is:

2021 = 43¹ × 47¹

Step-3: Factors of 2005

List of positive integer factors of 2005 that divides 2005 without a remainder.

1, 5, 401

Step-4: Factors of 2021

List of positive integer factors of 2021 that divides 2005 without a remainder.

1, 43, 47

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2005 and 2021. The biggest common factor number is the GCF number.
So the greatest common factor 2005 and 2021 is 1.

Also check out the Least Common Multiple of 2005 and 2021