What is the Greatest Common Factor of 2814 and 2821?

Greatest common factor (GCF) of 2814 and 2821 is 7.

GCF(2814,2821) = 7

We will now calculate the prime factors of 2814 and 2821, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2814 and 2821.

How to find the GCF of 2814 and 2821?

We will first find the prime factorization of 2814 and 2821. After we will calculate the factors of 2814 and 2821 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 2821

Prime factors of 2821 are 7, 13, 31. Prime factorization of 2821 in exponential form is:

2821 = 7¹ × 13¹ × 31¹

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 2821

List of positive integer factors of 2821 that divides 2814 without a remainder.

1, 7, 13, 31, 91, 217, 403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2814 and 2821. The biggest common factor number is the GCF number.
So the greatest common factor 2814 and 2821 is 7.

Also check out the Least Common Multiple of 2814 and 2821