What is the Greatest Common Factor of 34814 and 34827?

Greatest common factor (GCF) of 34814 and 34827 is 13.

GCF(34814,34827) = 13

We will now calculate the prime factors of 34814 and 34827, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34814 and 34827.

How to find the GCF of 34814 and 34827?

We will first find the prime factorization of 34814 and 34827. After we will calculate the factors of 34814 and 34827 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 34827

Prime factors of 34827 are 3, 13, 19, 47. Prime factorization of 34827 in exponential form is:

34827 = 3¹ × 13¹ × 19¹ × 47¹

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 34827

List of positive integer factors of 34827 that divides 34814 without a remainder.

1, 3, 13, 19, 39, 47, 57, 141, 247, 611, 741, 893, 1833, 2679, 11609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34814 and 34827. The biggest common factor number is the GCF number.
So the greatest common factor 34814 and 34827 is 13.

Also check out the Least Common Multiple of 34814 and 34827