Greatest Common Factor of 1574 and 1582

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 1574, 1582 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1574 and 1582 is 2.

GCF(1574,1582) = 2

GCF of 1574 and 1582

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

GCF of:
and

Greatest Common Factor of 1574 and 1582

GCF of 1574 and 1582 is 2

Prime Factorization of 1574


2 1574
787 787
1

Prime factors of 1574 are 2,787. Prime factorization of 1574 in exponential form is:

1574 = 21×7871

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

∴ So by taking common prime factors GCF of 1574 and 1582 is 2

Greatest Common Factor of 1574 and 1582 by matching factors method

Factors of 1574

List of positive integer factors of 1574 that divides 1574 without a remainder.

1,2,787,1574

Factors of 1582

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

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

Greatest Common Factor

We found the factors and prime factorization of 1574 and 1582. The biggest common factor number is the GCF number.
So the greatest common factor 1574 and 1582 is 2.

Also check out the Least Common Multiple of 1574 and 1582

Properties of GCF 1574 and 1582

(i) The GCF of 1574 and 1582 is associative

GCF of 1574 and 1582 = GCF of 1582 and 1574

Related Greatest Common Factor of 1574

Related Greatest Common Factor of 1582

Frequently Asked Questions on GCF of 1574 and 1582

1. What is the GCF of 1574 and 1582?

Answer: GCF of 1574 and 1582 is 2.

2. What are the Factors of 1574?

Answer: Factors of 1574 are 1, 2, 787, 1574. There are 4 integers that are factors of 1574. The greatest factor of 1574 is 1574.

3. 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.

4. How to Find the GCF of 1574 and 1582?

Answer:

Greatest Common Factor of 1574 and 1582 = 2

Step 1: Find the prime factorization of 1574

1574 = 2 x 787

Step 2: Find the prime factorization of 1582

1582 = 2 x 7 x 113

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 1574 and 1582 is 2