Greatest Common Factor of 1582 and 1584

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 1582, 1584 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1582 and 1584 is 2.

GCF(1582,1584) = 2

GCF of 1582 and 1584

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

GCF of:
and

Greatest Common Factor of 1582 and 1584

GCF of 1582 and 1584 is 2

Prime Factorization of 1582


2 1582
7 791
113 113
1

Prime factors of 1582 are 2,7,113. Prime factorization of 1582 in exponential form is:

1582 = 21×71×1131

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

∴ So by taking common prime factors GCF of 1582 and 1584 is 2

Greatest Common Factor of 1582 and 1584 by matching factors method

Factors of 1582

List of positive integer factors of 1582 that divides 1582 without a remainder.

1,2,7,14,113,226,791,1582

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

Greatest Common Factor

We found the factors and prime factorization of 1582 and 1584. The biggest common factor number is the GCF number.
So the greatest common factor 1582 and 1584 is 2.

Also check out the Least Common Multiple of 1582 and 1584

Properties of GCF 1582 and 1584

(i) The GCF of 1582 and 1584 is associative

GCF of 1582 and 1584 = GCF of 1584 and 1582

Related Greatest Common Factor of 1582

Related Greatest Common Factor of 1584

Frequently Asked Questions on GCF of 1582 and 1584

1. What is the GCF of 1582 and 1584?

Answer: GCF of 1582 and 1584 is 2.

2. What are the Factors of 1582?

Answer: Factors of 1582 are 1, 2, 7, 14, 113, 226, 791, 1582. There are 8 integers that are factors of 1582. The greatest factor of 1582 is 1582.

3. 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.

4. How to Find the GCF of 1582 and 1584?

Answer:

Greatest Common Factor of 1582 and 1584 = 2

Step 1: Find the prime factorization of 1582

1582 = 2 x 7 x 113

Step 2: Find the prime factorization of 1584

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

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

GCF = 2

Step 4: Therefore, the greatest common factor of 1582 and 1584 is 2