What is the Greatest Common Factor of 1584 and 1600?

Greatest common factor (GCF) of 1584 and 1600 is 16.

GCF(1584,1600) = 16

We will now calculate the prime factors of 1584 and 1600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1584 and 1600.

How to find the GCF of 1584 and 1600?

We will first find the prime factorization of 1584 and 1600. After we will calculate the factors of 1584 and 1600 and find the biggest common factor number .

Step-1: Prime Factorization of 1584

Prime factors of 1584 are 2, 3, 11. Prime factorization of 1584 in exponential form is:

1584 = 2⁴ × 3² × 11¹

Step-2: Prime Factorization of 1600

Prime factors of 1600 are 2, 5. Prime factorization of 1600 in exponential form is:

1600 = 2⁶ × 5²

Step-3: Factors of 1584

List of positive integer factors of 1584 that divides 1584 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792

Step-4: Factors of 1600

List of positive integer factors of 1600 that divides 1584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1584 and 1600. The biggest common factor number is the GCF number.
So the greatest common factor 1584 and 1600 is 16.

Also check out the Least Common Multiple of 1584 and 1600