What is the Greatest Common Factor of 18400 and 18414?

Greatest common factor (GCF) of 18400 and 18414 is 2.

GCF(18400,18414) = 2

We will now calculate the prime factors of 18400 and 18414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18400 and 18414.

How to find the GCF of 18400 and 18414?

We will first find the prime factorization of 18400 and 18414. After we will calculate the factors of 18400 and 18414 and find the biggest common factor number .

Step-1: Prime Factorization of 18400

Prime factors of 18400 are 2, 5, 23. Prime factorization of 18400 in exponential form is:

18400 = 2⁵ × 5² × 23¹

Step-2: Prime Factorization of 18414

Prime factors of 18414 are 2, 3, 11, 31. Prime factorization of 18414 in exponential form is:

18414 = 2¹ × 3³ × 11¹ × 31¹

Step-3: Factors of 18400

List of positive integer factors of 18400 that divides 18400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 80, 92, 100, 115, 160, 184, 200, 230, 368, 400, 460, 575, 736, 800, 920, 1150, 1840, 2300, 3680, 4600, 9200

Step-4: Factors of 18414

List of positive integer factors of 18414 that divides 18400 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 31, 33, 54, 62, 66, 93, 99, 186, 198, 279, 297, 341, 558, 594, 682, 837, 1023, 1674, 2046, 3069, 6138, 9207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18400 and 18414. The biggest common factor number is the GCF number.
So the greatest common factor 18400 and 18414 is 2.

Also check out the Least Common Multiple of 18400 and 18414