What is the Greatest Common Factor of 2814 and 2822?

Greatest common factor (GCF) of 2814 and 2822 is 2.

GCF(2814,2822) = 2

We will now calculate the prime factors of 2814 and 2822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2814 and 2822.

How to find the GCF of 2814 and 2822?

We will first find the prime factorization of 2814 and 2822. After we will calculate the factors of 2814 and 2822 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 2822

Prime factors of 2822 are 2, 17, 83. Prime factorization of 2822 in exponential form is:

2822 = 2¹ × 17¹ × 83¹

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 2822

List of positive integer factors of 2822 that divides 2814 without a remainder.

1, 2, 17, 34, 83, 166, 1411

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2814 and 2822. The biggest common factor number is the GCF number.
So the greatest common factor 2814 and 2822 is 2.

Also check out the Least Common Multiple of 2814 and 2822