What is the Greatest Common Factor of 27904 and 27914?

Greatest common factor (GCF) of 27904 and 27914 is 2.

GCF(27904,27914) = 2

We will now calculate the prime factors of 27904 and 27914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27904 and 27914.

How to find the GCF of 27904 and 27914?

We will first find the prime factorization of 27904 and 27914. After we will calculate the factors of 27904 and 27914 and find the biggest common factor number .

Step-1: Prime Factorization of 27904

Prime factors of 27904 are 2, 109. Prime factorization of 27904 in exponential form is:

27904 = 2⁸ × 109¹

Step-2: Prime Factorization of 27914

Prime factors of 27914 are 2, 17, 821. Prime factorization of 27914 in exponential form is:

27914 = 2¹ × 17¹ × 821¹

Step-3: Factors of 27904

List of positive integer factors of 27904 that divides 27904 without a remainder.

1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 256, 436, 872, 1744, 3488, 6976, 13952

Step-4: Factors of 27914

List of positive integer factors of 27914 that divides 27904 without a remainder.

1, 2, 17, 34, 821, 1642, 13957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27904 and 27914. The biggest common factor number is the GCF number.
So the greatest common factor 27904 and 27914 is 2.

Also check out the Least Common Multiple of 27904 and 27914