What is the Greatest Common Factor of 30814 and 30821?

Greatest common factor (GCF) of 30814 and 30821 is 7.

GCF(30814,30821) = 7

We will now calculate the prime factors of 30814 and 30821, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30814 and 30821.

How to find the GCF of 30814 and 30821?

We will first find the prime factorization of 30814 and 30821. After we will calculate the factors of 30814 and 30821 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 30821

Prime factors of 30821 are 7, 17, 37. Prime factorization of 30821 in exponential form is:

30821 = 7² × 17¹ × 37¹

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 30821

List of positive integer factors of 30821 that divides 30814 without a remainder.

1, 7, 17, 37, 49, 119, 259, 629, 833, 1813, 4403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30814 and 30821. The biggest common factor number is the GCF number.
So the greatest common factor 30814 and 30821 is 7.

Also check out the Least Common Multiple of 30814 and 30821