Factors of 1742
2026-02-28 13:35 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1742, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1742?

The numbers that divide 1742 evenly are known as factors of 1742.

A factor of 1742 is a number that divides the number without a remainder.

The factors of 1742 are 1, 2, 871, and 1742.

Negative factors of 1742: -1, -2, -871, and -1742.

Prime factors of 1742: 2 and 871.

Prime factorization of 1742: 2 × 871.

The sum of factors of 1742: 1 + 2 + 871 + 1742 = 2616

How to Find Factors of 1742?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1742. Identifying the numbers which are multiplied to get the number 1742 is the multiplication method.

Step 1: Multiply 1742 by 1, 1742 × 1 = 1742.

Step 2: Check for other numbers that give 1742 after multiplying 2 × 871 = 1742

Therefore, the positive factor pairs of 1742 are: (1, 1742) and (2, 871).

All these factor pairs result in 1742.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method 

Step 1: Divide 1742 by 1, 1742 ÷ 1 = 1742.

Step 2: Continue dividing 1742 by the numbers until the remainder becomes 0.

1742 ÷ 1 = 1742

1742 ÷ 2 = 871

Therefore, the factors of 1742 are: 1, 2, 871, 1742.

Prime Factors and Prime Factorization

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 1742 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1742 ÷ 2 = 871

871 ÷ 871 = 1

The prime factors of 1742 are 2 and 871.

The prime factorization of 1742 is: 2 × 871.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows 

Step 1: Firstly, 1742 is divided by 2 to get 871.

Step 2: 871 is a prime number, so it cannot be divided further.

So, the prime factorization of 1742 is: 2 × 871.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 1742: (1, 1742), (2, 871).

Negative factor pairs of 1742: (-1, -1742), (-2, -871).

Common Mistakes and How to Avoid Them in Factors of 1742

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 1742 tickets and 2 ticket counters. How will they distribute it equally?

Okay, lets begin

They will get 871 tickets each.

Explanation

To distribute the tickets equally, we need to divide the total tickets with the number of counters.

1742/2 = 871

Well explained 👍

Problem 2

A rectangular garden has a length of 2 meters and a total area of 1742 square meters. Find the width?

Okay, lets begin

871 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

1742 = 2 × width

To find the value of width, we need to shift 2 to the left side.

1742/2 = width

Width = 871.

Well explained 👍

Problem 3

There are 871 chairs and 1742 people. How many people will share one chair?

Okay, lets begin

Each chair will have 2 people.

Explanation

To find the number of people sharing each chair, divide the total people by the number of chairs.

1742/871 = 2

Well explained 👍

Problem 4

In a class, there are 1742 students, and 2 groups. How many students are there in each group?

Okay, lets begin

There are 871 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

1742/2 = 871

Well explained 👍

Problem 5

1742 books need to be arranged in 2 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 871 books.

Explanation

Divide total books with shelves.

1742/2 = 871

Well explained 👍

FAQs on Factors of 1742

1.What are the factors of 1742?

1, 2, 871, 1742 are the factors of 1742.

2.Mention the prime factors of 1742.

The prime factors of 1742 are 2 × 871.

3.Is 1742 a multiple of 2?

4.Mention the factor pairs of 1742?

(1, 1742) and (2, 871) are the factor pairs of 1742.

5.What is the square of 1742?

The square of 1742 is 3034564.

Important Glossaries for Factors of 1742

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1742 are 1, 2, 871, and 1742.
  • Prime factors: The factors which are prime numbers. For example, 2 and 871 are prime factors of 1742.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1742 are (1, 1742) and (2, 871).
  • Prime factorization: The expression of a number as the product of its prime factors. For 1742, it is 2 × 871.
  • Multiple: A number that can be divided by another number without a remainder. For example, 1742 is a multiple of 2.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.