What is the Greatest Common Factor of 2034 and 2040?

Greatest common factor (GCF) of 2034 and 2040 is 6.

GCF(2034,2040) = 6

We will now calculate the prime factors of 2034 and 2040, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2034 and 2040.

How to find the GCF of 2034 and 2040?

We will first find the prime factorization of 2034 and 2040. After we will calculate the factors of 2034 and 2040 and find the biggest common factor number .

Step-1: Prime Factorization of 2034

Prime factors of 2034 are 2, 3, 113. Prime factorization of 2034 in exponential form is:

2034 = 2¹ × 3² × 113¹

Step-2: Prime Factorization of 2040

Prime factors of 2040 are 2, 3, 5, 17. Prime factorization of 2040 in exponential form is:

2040 = 2³ × 3¹ × 5¹ × 17¹

Step-3: Factors of 2034

List of positive integer factors of 2034 that divides 2034 without a remainder.

1, 2, 3, 6, 9, 18, 113, 226, 339, 678, 1017

Step-4: Factors of 2040

List of positive integer factors of 2040 that divides 2034 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2034 and 2040. The biggest common factor number is the GCF number.
So the greatest common factor 2034 and 2040 is 6.

Also check out the Least Common Multiple of 2034 and 2040