What is the Greatest Common Factor of 27800 and 27810?

Greatest common factor (GCF) of 27800 and 27810 is 10.

GCF(27800,27810) = 10

We will now calculate the prime factors of 27800 and 27810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27800 and 27810.

How to find the GCF of 27800 and 27810?

We will first find the prime factorization of 27800 and 27810. After we will calculate the factors of 27800 and 27810 and find the biggest common factor number .

Step-1: Prime Factorization of 27800

Prime factors of 27800 are 2, 5, 139. Prime factorization of 27800 in exponential form is:

27800 = 2³ × 5² × 139¹

Step-2: Prime Factorization of 27810

Prime factors of 27810 are 2, 3, 5, 103. Prime factorization of 27810 in exponential form is:

27810 = 2¹ × 3³ × 5¹ × 103¹

Step-3: Factors of 27800

List of positive integer factors of 27800 that divides 27800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 139, 200, 278, 556, 695, 1112, 1390, 2780, 3475, 5560, 6950, 13900

Step-4: Factors of 27810

List of positive integer factors of 27810 that divides 27800 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 103, 135, 206, 270, 309, 515, 618, 927, 1030, 1545, 1854, 2781, 3090, 4635, 5562, 9270, 13905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27800 and 27810. The biggest common factor number is the GCF number.
So the greatest common factor 27800 and 27810 is 10.

Also check out the Least Common Multiple of 27800 and 27810