What is the Greatest Common Factor of 8382 and 8400?

Greatest common factor (GCF) of 8382 and 8400 is 6.

GCF(8382,8400) = 6

We will now calculate the prime factors of 8382 and 8400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8382 and 8400.

How to find the GCF of 8382 and 8400?

We will first find the prime factorization of 8382 and 8400. After we will calculate the factors of 8382 and 8400 and find the biggest common factor number .

Step-1: Prime Factorization of 8382

Prime factors of 8382 are 2, 3, 11, 127. Prime factorization of 8382 in exponential form is:

8382 = 2¹ × 3¹ × 11¹ × 127¹

Step-2: 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-3: Factors of 8382

List of positive integer factors of 8382 that divides 8382 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 127, 254, 381, 762, 1397, 2794, 4191

Step-4: Factors of 8400

List of positive integer factors of 8400 that divides 8382 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8382 and 8400. The biggest common factor number is the GCF number.
So the greatest common factor 8382 and 8400 is 6.

Also check out the Least Common Multiple of 8382 and 8400