What is the Greatest Common Factor of 34814 and 34822?

Greatest common factor (GCF) of 34814 and 34822 is 2.

GCF(34814,34822) = 2

We will now calculate the prime factors of 34814 and 34822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34814 and 34822.

How to find the GCF of 34814 and 34822?

We will first find the prime factorization of 34814 and 34822. After we will calculate the factors of 34814 and 34822 and find the biggest common factor number .

Step-1: Prime Factorization of 34814

Prime factors of 34814 are 2, 13, 103. Prime factorization of 34814 in exponential form is:

34814 = 2¹ × 13² × 103¹

Step-2: Prime Factorization of 34822

Prime factors of 34822 are 2, 23, 757. Prime factorization of 34822 in exponential form is:

34822 = 2¹ × 23¹ × 757¹

Step-3: Factors of 34814

List of positive integer factors of 34814 that divides 34814 without a remainder.

1, 2, 13, 26, 103, 169, 206, 338, 1339, 2678, 17407

Step-4: Factors of 34822

List of positive integer factors of 34822 that divides 34814 without a remainder.

1, 2, 23, 46, 757, 1514, 17411

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34814 and 34822. The biggest common factor number is the GCF number.
So the greatest common factor 34814 and 34822 is 2.

Also check out the Least Common Multiple of 34814 and 34822