What is the Greatest Common Factor of 20400 and 20408?

Greatest common factor (GCF) of 20400 and 20408 is 8.

GCF(20400,20408) = 8

We will now calculate the prime factors of 20400 and 20408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20400 and 20408.

How to find the GCF of 20400 and 20408?

We will first find the prime factorization of 20400 and 20408. After we will calculate the factors of 20400 and 20408 and find the biggest common factor number .

Step-1: Prime Factorization of 20400

Prime factors of 20400 are 2, 3, 5, 17. Prime factorization of 20400 in exponential form is:

20400 = 2⁴ × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 20408

Prime factors of 20408 are 2, 2551. Prime factorization of 20408 in exponential form is:

20408 = 2³ × 2551¹

Step-3: Factors of 20400

List of positive integer factors of 20400 that divides 20400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200

Step-4: Factors of 20408

List of positive integer factors of 20408 that divides 20400 without a remainder.

1, 2, 4, 8, 2551, 5102, 10204

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20400 and 20408. The biggest common factor number is the GCF number.
So the greatest common factor 20400 and 20408 is 8.

Also check out the Least Common Multiple of 20400 and 20408