What is the Greatest Common Factor of 2814 and 2834?

Greatest common factor (GCF) of 2814 and 2834 is 2.

GCF(2814,2834) = 2

We will now calculate the prime factors of 2814 and 2834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2814 and 2834.

How to find the GCF of 2814 and 2834?

We will first find the prime factorization of 2814 and 2834. After we will calculate the factors of 2814 and 2834 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 2834

Prime factors of 2834 are 2, 13, 109. Prime factorization of 2834 in exponential form is:

2834 = 2¹ × 13¹ × 109¹

Step-3: Factors of 2814

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

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

Step-4: Factors of 2834

List of positive integer factors of 2834 that divides 2814 without a remainder.

1, 2, 13, 26, 109, 218, 1417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2814 and 2834. The biggest common factor number is the GCF number.
So the greatest common factor 2814 and 2834 is 2.

Also check out the Least Common Multiple of 2814 and 2834