What is the Greatest Common Factor of 1584 and 1604?

Greatest common factor (GCF) of 1584 and 1604 is 4.

GCF(1584,1604) = 4

We will now calculate the prime factors of 1584 and 1604, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1584 and 1604.

How to find the GCF of 1584 and 1604?

We will first find the prime factorization of 1584 and 1604. After we will calculate the factors of 1584 and 1604 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 1604

Prime factors of 1604 are 2, 401. Prime factorization of 1604 in exponential form is:

1604 = 2² × 401¹

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 1604

List of positive integer factors of 1604 that divides 1584 without a remainder.

1, 2, 4, 401, 802

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1584 and 1604. The biggest common factor number is the GCF number.
So the greatest common factor 1584 and 1604 is 4.

Also check out the Least Common Multiple of 1584 and 1604