Greatest Common Factor of 1584 and 1590

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1584, 1590 i.e. 6 largest integer by which both the numbers can be divided.

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

GCF(1584,1590) = 6

GCF of 1584 and 1590

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1584 and 1590

GCF of 1584 and 1590 is 6

Prime Factorization of 1584


2 1584
2 792
2 396
2 198
3 99
3 33
11 11
1

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

1584 = 24×32×111

Prime Factorization of 1590


2 1590
3 795
5 265
53 53
1

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

1590 = 21×31×51×531

∴ So by taking common prime factors GCF of 1584 and 1590 is 6

Greatest Common Factor of 1584 and 1590 by matching factors method

Factors of 1584

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

1,2,3,4,6,8,9,11,12,16,18,22,24,33,36,44,48,66,72,88,99,132,144,176,198,264,396,528,792,1584

Factors of 1590

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

1,2,3,5,6,10,15,30,53,106,159,265,318,530,795,1590

Greatest Common Factor

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

Properties of GCF 1584 and 1590

(i) The GCF of 1584 and 1590 is associative

GCF of 1584 and 1590 = GCF of 1590 and 1584

Related Greatest Common Factor of 1584

Related Greatest Common Factor of 1590

Frequently Asked Questions on GCF of 1584 and 1590

1. What is the GCF of 1584 and 1590?

Answer: GCF of 1584 and 1590 is 6.

2. What are the Factors of 1584?

Answer: Factors of 1584 are 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, 1584. There are 30 integers that are factors of 1584. The greatest factor of 1584 is 1584.

3. What are the Factors of 1590?

Answer: Factors of 1590 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590. There are 16 integers that are factors of 1590. The greatest factor of 1590 is 1590.

4. How to Find the GCF of 1584 and 1590?

Answer:

Greatest Common Factor of 1584 and 1590 = 6

Step 1: Find the prime factorization of 1584

1584 = 2 x 2 x 2 x 2 x 3 x 3 x 11

Step 2: Find the prime factorization of 1590

1590 = 2 x 3 x 5 x 53

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 1584 and 1590 is 6