What is the Greatest Common Factor of 27814 and 27820?

Greatest common factor (GCF) of 27814 and 27820 is 2.

GCF(27814,27820) = 2

We will now calculate the prime factors of 27814 and 27820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27814 and 27820.

How to find the GCF of 27814 and 27820?

We will first find the prime factorization of 27814 and 27820. After we will calculate the factors of 27814 and 27820 and find the biggest common factor number .

Step-1: Prime Factorization of 27814

Prime factors of 27814 are 2, 13907. Prime factorization of 27814 in exponential form is:

27814 = 2¹ × 13907¹

Step-2: Prime Factorization of 27820

Prime factors of 27820 are 2, 5, 13, 107. Prime factorization of 27820 in exponential form is:

27820 = 2² × 5¹ × 13¹ × 107¹

Step-3: Factors of 27814

List of positive integer factors of 27814 that divides 27814 without a remainder.

1, 2, 13907

Step-4: Factors of 27820

List of positive integer factors of 27820 that divides 27814 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 107, 130, 214, 260, 428, 535, 1070, 1391, 2140, 2782, 5564, 6955, 13910

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27814 and 27820. The biggest common factor number is the GCF number.
So the greatest common factor 27814 and 27820 is 2.

Also check out the Least Common Multiple of 27814 and 27820