Greatest Common Factor of 1582 and 1586

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, 1586 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1582 and 1586 is 2.

GCF(1582,1586) = 2

GCF of 1582 and 1586

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

GCF of:
and

Greatest Common Factor of 1582 and 1586

GCF of 1582 and 1586 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 1586


2 1586
13 793
61 61
1

Prime factors of 1586 are 2,13,61. Prime factorization of 1586 in exponential form is:

1586 = 21×131×611

∴ So by taking common prime factors GCF of 1582 and 1586 is 2

Greatest Common Factor of 1582 and 1586 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 1586

List of positive integer factors of 1586 that divides 1586 without a remainder.

1,2,13,26,61,122,793,1586

Greatest Common Factor

We found the factors and prime factorization of 1582 and 1586. The biggest common factor number is the GCF number.
So the greatest common factor 1582 and 1586 is 2.

Also check out the Least Common Multiple of 1582 and 1586

Properties of GCF 1582 and 1586

(i) The GCF of 1582 and 1586 is associative

GCF of 1582 and 1586 = GCF of 1586 and 1582

Related Greatest Common Factor of 1582

Related Greatest Common Factor of 1586

Frequently Asked Questions on GCF of 1582 and 1586

1. What is the GCF of 1582 and 1586?

Answer: GCF of 1582 and 1586 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 1586?

Answer: Factors of 1586 are 1, 2, 13, 26, 61, 122, 793, 1586. There are 8 integers that are factors of 1586. The greatest factor of 1586 is 1586.

4. How to Find the GCF of 1582 and 1586?

Answer:

Greatest Common Factor of 1582 and 1586 = 2

Step 1: Find the prime factorization of 1582

1582 = 2 x 7 x 113

Step 2: Find the prime factorization of 1586

1586 = 2 x 13 x 61

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 1586 is 2