What is the Greatest Common Factor of 2798 and 2814?

Greatest common factor (GCF) of 2798 and 2814 is 2.

GCF(2798,2814) = 2

We will now calculate the prime factors of 2798 and 2814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2798 and 2814.

How to find the GCF of 2798 and 2814?

We will first find the prime factorization of 2798 and 2814. After we will calculate the factors of 2798 and 2814 and find the biggest common factor number .

Step-1: Prime Factorization of 2798

Prime factors of 2798 are 2, 1399. Prime factorization of 2798 in exponential form is:

2798 = 2¹ × 1399¹

Step-2: Prime Factorization of 2814

Prime factors of 2814 are 2, 3, 7, 67. Prime factorization of 2814 in exponential form is:

2814 = 2¹ × 3¹ × 7¹ × 67¹

Step-3: Factors of 2798

List of positive integer factors of 2798 that divides 2798 without a remainder.

1, 2, 1399

Step-4: Factors of 2814

List of positive integer factors of 2814 that divides 2798 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2798 and 2814. The biggest common factor number is the GCF number.
So the greatest common factor 2798 and 2814 is 2.

Also check out the Least Common Multiple of 2798 and 2814