What is the Greatest Common Factor of 30814 and 30822?

Greatest common factor (GCF) of 30814 and 30822 is 2.

GCF(30814,30822) = 2

We will now calculate the prime factors of 30814 and 30822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30814 and 30822.

How to find the GCF of 30814 and 30822?

We will first find the prime factorization of 30814 and 30822. After we will calculate the factors of 30814 and 30822 and find the biggest common factor number .

Step-1: Prime Factorization of 30814

Prime factors of 30814 are 2, 7, 31, 71. Prime factorization of 30814 in exponential form is:

30814 = 2¹ × 7¹ × 31¹ × 71¹

Step-2: Prime Factorization of 30822

Prime factors of 30822 are 2, 3, 11, 467. Prime factorization of 30822 in exponential form is:

30822 = 2¹ × 3¹ × 11¹ × 467¹

Step-3: Factors of 30814

List of positive integer factors of 30814 that divides 30814 without a remainder.

1, 2, 7, 14, 31, 62, 71, 142, 217, 434, 497, 994, 2201, 4402, 15407

Step-4: Factors of 30822

List of positive integer factors of 30822 that divides 30814 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 467, 934, 1401, 2802, 5137, 10274, 15411

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30814 and 30822. The biggest common factor number is the GCF number.
So the greatest common factor 30814 and 30822 is 2.

Also check out the Least Common Multiple of 30814 and 30822