What is the Greatest Common Factor of 27900 and 27914?

Greatest common factor (GCF) of 27900 and 27914 is 2.

GCF(27900,27914) = 2

We will now calculate the prime factors of 27900 and 27914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27900 and 27914.

How to find the GCF of 27900 and 27914?

We will first find the prime factorization of 27900 and 27914. After we will calculate the factors of 27900 and 27914 and find the biggest common factor number .

Step-1: Prime Factorization of 27900

Prime factors of 27900 are 2, 3, 5, 31. Prime factorization of 27900 in exponential form is:

27900 = 2² × 3² × 5² × 31¹

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 27900

List of positive integer factors of 27900 that divides 27900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 31, 36, 45, 50, 60, 62, 75, 90, 93, 100, 124, 150, 155, 180, 186, 225, 279, 300, 310, 372, 450, 465, 558, 620, 775, 900, 930, 1116, 1395, 1550, 1860, 2325, 2790, 3100, 4650, 5580, 6975, 9300, 13950

Step-4: Factors of 27914

List of positive integer factors of 27914 that divides 27900 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27900 and 27914. The biggest common factor number is the GCF number.
So the greatest common factor 27900 and 27914 is 2.

Also check out the Least Common Multiple of 27900 and 27914