What is the Greatest Common Factor of 23400 and 23414?

Greatest common factor (GCF) of 23400 and 23414 is 2.

GCF(23400,23414) = 2

We will now calculate the prime factors of 23400 and 23414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23400 and 23414.

How to find the GCF of 23400 and 23414?

We will first find the prime factorization of 23400 and 23414. After we will calculate the factors of 23400 and 23414 and find the biggest common factor number .

Step-1: Prime Factorization of 23400

Prime factors of 23400 are 2, 3, 5, 13. Prime factorization of 23400 in exponential form is:

23400 = 2³ × 3² × 5² × 13¹

Step-2: Prime Factorization of 23414

Prime factors of 23414 are 2, 23, 509. Prime factorization of 23414 in exponential form is:

23414 = 2¹ × 23¹ × 509¹

Step-3: Factors of 23400

List of positive integer factors of 23400 that divides 23400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 25, 26, 30, 36, 39, 40, 45, 50, 52, 60, 65, 72, 75, 78, 90, 100, 104, 117, 120, 130, 150, 156, 180, 195, 200, 225, 234, 260, 300, 312, 325, 360, 390, 450, 468, 520, 585, 600, 650, 780, 900, 936, 975, 1170, 1300, 1560, 1800, 1950, 2340, 2600, 2925, 3900, 4680, 5850, 7800, 11700

Step-4: Factors of 23414

List of positive integer factors of 23414 that divides 23400 without a remainder.

1, 2, 23, 46, 509, 1018, 11707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23400 and 23414. The biggest common factor number is the GCF number.
So the greatest common factor 23400 and 23414 is 2.

Also check out the Least Common Multiple of 23400 and 23414