What is the Greatest Common Factor of 5382 and 5400?

Greatest common factor (GCF) of 5382 and 5400 is 18.

GCF(5382,5400) = 18

We will now calculate the prime factors of 5382 and 5400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5382 and 5400.

How to find the GCF of 5382 and 5400?

We will first find the prime factorization of 5382 and 5400. After we will calculate the factors of 5382 and 5400 and find the biggest common factor number .

Step-1: Prime Factorization of 5382

Prime factors of 5382 are 2, 3, 13, 23. Prime factorization of 5382 in exponential form is:

5382 = 2¹ × 3² × 13¹ × 23¹

Step-2: Prime Factorization of 5400

Prime factors of 5400 are 2, 3, 5. Prime factorization of 5400 in exponential form is:

5400 = 2³ × 3³ × 5²

Step-3: Factors of 5382

List of positive integer factors of 5382 that divides 5382 without a remainder.

1, 2, 3, 6, 9, 13, 18, 23, 26, 39, 46, 69, 78, 117, 138, 207, 234, 299, 414, 598, 897, 1794, 2691

Step-4: Factors of 5400

List of positive integer factors of 5400 that divides 5382 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5382 and 5400. The biggest common factor number is the GCF number.
So the greatest common factor 5382 and 5400 is 18.

Also check out the Least Common Multiple of 5382 and 5400