Greatest Common Factor of 1582 and 1589

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, 1589 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1582 and 1589 is 7.

GCF(1582,1589) = 7

GCF of 1582 and 1589

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

GCF of:
and

Greatest Common Factor of 1582 and 1589

GCF of 1582 and 1589 is 7

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 1589


7 1589
227 227
1

Prime factors of 1589 are 7,227. Prime factorization of 1589 in exponential form is:

1589 = 71×2271

∴ So by taking common prime factors GCF of 1582 and 1589 is 7

Greatest Common Factor of 1582 and 1589 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 1589

List of positive integer factors of 1589 that divides 1589 without a remainder.

1,7,227,1589

Greatest Common Factor

We found the factors and prime factorization of 1582 and 1589. The biggest common factor number is the GCF number.
So the greatest common factor 1582 and 1589 is 7.

Also check out the Least Common Multiple of 1582 and 1589

Properties of GCF 1582 and 1589

(i) The GCF of 1582 and 1589 is associative

GCF of 1582 and 1589 = GCF of 1589 and 1582

Related Greatest Common Factor of 1582

Related Greatest Common Factor of 1589

Frequently Asked Questions on GCF of 1582 and 1589

1. What is the GCF of 1582 and 1589?

Answer: GCF of 1582 and 1589 is 7.

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 1589?

Answer: Factors of 1589 are 1, 7, 227, 1589. There are 4 integers that are factors of 1589. The greatest factor of 1589 is 1589.

4. How to Find the GCF of 1582 and 1589?

Answer:

Greatest Common Factor of 1582 and 1589 = 7

Step 1: Find the prime factorization of 1582

1582 = 2 x 7 x 113

Step 2: Find the prime factorization of 1589

1589 = 7 x 227

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

GCF = 7

Step 4: Therefore, the greatest common factor of 1582 and 1589 is 7