What is the Greatest Common Factor of 8400 and 8409?

Greatest common factor (GCF) of 8400 and 8409 is 3.

GCF(8400,8409) = 3

We will now calculate the prime factors of 8400 and 8409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8400 and 8409.

How to find the GCF of 8400 and 8409?

We will first find the prime factorization of 8400 and 8409. After we will calculate the factors of 8400 and 8409 and find the biggest common factor number .

Step-1: Prime Factorization of 8400

Prime factors of 8400 are 2, 3, 5, 7. Prime factorization of 8400 in exponential form is:

8400 = 2⁴ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 8409

Prime factors of 8409 are 3, 2803. Prime factorization of 8409 in exponential form is:

8409 = 3¹ × 2803¹

Step-3: Factors of 8400

List of positive integer factors of 8400 that divides 8400 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200

Step-4: Factors of 8409

List of positive integer factors of 8409 that divides 8400 without a remainder.

1, 3, 2803

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8400 and 8409. The biggest common factor number is the GCF number.
So the greatest common factor 8400 and 8409 is 3.

Also check out the Least Common Multiple of 8400 and 8409