What is the Greatest Common Factor of 2074 and 2082?

Greatest common factor (GCF) of 2074 and 2082 is 2.

GCF(2074,2082) = 2

We will now calculate the prime factors of 2074 and 2082, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2074 and 2082.

How to find the GCF of 2074 and 2082?

We will first find the prime factorization of 2074 and 2082. After we will calculate the factors of 2074 and 2082 and find the biggest common factor number .

Step-1: Prime Factorization of 2074

Prime factors of 2074 are 2, 17, 61. Prime factorization of 2074 in exponential form is:

2074 = 2¹ × 17¹ × 61¹

Step-2: Prime Factorization of 2082

Prime factors of 2082 are 2, 3, 347. Prime factorization of 2082 in exponential form is:

2082 = 2¹ × 3¹ × 347¹

Step-3: Factors of 2074

List of positive integer factors of 2074 that divides 2074 without a remainder.

1, 2, 17, 34, 61, 122, 1037

Step-4: Factors of 2082

List of positive integer factors of 2082 that divides 2074 without a remainder.

1, 2, 3, 6, 347, 694, 1041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2074 and 2082. The biggest common factor number is the GCF number.
So the greatest common factor 2074 and 2082 is 2.

Also check out the Least Common Multiple of 2074 and 2082