What is the Greatest Common Factor of 61800 and 61814?

Greatest common factor (GCF) of 61800 and 61814 is 2.

GCF(61800,61814) = 2

We will now calculate the prime factors of 61800 and 61814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61800 and 61814.

How to find the GCF of 61800 and 61814?

We will first find the prime factorization of 61800 and 61814. After we will calculate the factors of 61800 and 61814 and find the biggest common factor number .

Step-1: Prime Factorization of 61800

Prime factors of 61800 are 2, 3, 5, 103. Prime factorization of 61800 in exponential form is:

61800 = 2³ × 3¹ × 5² × 103¹

Step-2: Prime Factorization of 61814

Prime factors of 61814 are 2, 31, 997. Prime factorization of 61814 in exponential form is:

61814 = 2¹ × 31¹ × 997¹

Step-3: Factors of 61800

List of positive integer factors of 61800 that divides 61800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 103, 120, 150, 200, 206, 300, 309, 412, 515, 600, 618, 824, 1030, 1236, 1545, 2060, 2472, 2575, 3090, 4120, 5150, 6180, 7725, 10300, 12360, 15450, 20600, 30900

Step-4: Factors of 61814

List of positive integer factors of 61814 that divides 61800 without a remainder.

1, 2, 31, 62, 997, 1994, 30907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61800 and 61814. The biggest common factor number is the GCF number.
So the greatest common factor 61800 and 61814 is 2.

Also check out the Least Common Multiple of 61800 and 61814