What is the Greatest Common Factor of 1584 and 1590?

Greatest common factor (GCF) of 1584 and 1590 is 6.

GCF(1584,1590) = 6

We will now calculate the prime factors of 1584 and 1590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1584 and 1590.

How to find the GCF of 1584 and 1590?

We will first find the prime factorization of 1584 and 1590. After we will calculate the factors of 1584 and 1590 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 1590

Prime factors of 1590 are 2, 3, 5, 53. Prime factorization of 1590 in exponential form is:

1590 = 2¹ × 3¹ × 5¹ × 53¹

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 1590

List of positive integer factors of 1590 that divides 1584 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1584 and 1590. The biggest common factor number is the GCF number.
So the greatest common factor 1584 and 1590 is 6.

Also check out the Least Common Multiple of 1584 and 1590