What is the Greatest Common Factor of 2074 and 2080?

Greatest common factor (GCF) of 2074 and 2080 is 2.

GCF(2074,2080) = 2

We will now calculate the prime factors of 2074 and 2080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2074 and 2080.

How to find the GCF of 2074 and 2080?

We will first find the prime factorization of 2074 and 2080. After we will calculate the factors of 2074 and 2080 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 2080

Prime factors of 2080 are 2, 5, 13. Prime factorization of 2080 in exponential form is:

2080 = 2⁵ × 5¹ × 13¹

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 2080

List of positive integer factors of 2080 that divides 2074 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 416, 520, 1040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2074 and 2080. The biggest common factor number is the GCF number.
So the greatest common factor 2074 and 2080 is 2.

Also check out the Least Common Multiple of 2074 and 2080