Factors of 1048
2026-02-28 08:44 Diff

220 Learners

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 1048, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 1048?

The numbers that divide 1048 evenly are known as factors of 1048.

A factor of 1048 is a number that divides the number without remainder.

The factors of 1048 are 1, 2, 4, 8, 131, 262, 524, and 1048.

Negative factors of 1048: -1, -2, -4, -8, -131, -262, -524, and -1048.

Prime factors of 1048: 2 and 131.

Prime factorization of 1048: 23 × 131.

The sum of factors of 1048: 1 + 2 + 4 + 8 + 131 + 262 + 524 + 1048 = 1980

How to Find Factors of 1048?

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

  • Finding factors using multiplication
  • Finding factors using division method
  • Prime factors and Prime factorization

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1048. Identifying the numbers which are multiplied to get the number 1048 is the multiplication method.

Step 1: Multiply 1048 by 1, 1048 × 1 = 1048.

Step 2: Check for other numbers that give 1048 after multiplying

2 × 524 = 1048

4 × 262 = 1048

8 × 131 = 1048

Therefore, the positive factor pairs of 1048 are: (1, 1048), (2, 524), (4, 262), (8, 131). All these factor pairs result in 1048. For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the 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 1048 by 1, 1048 ÷ 1 = 1048.

Step 2: Continue dividing 1048 by the numbers until the remainder becomes 0.

1048 ÷ 1 = 1048

1048 ÷ 2 = 524

1048 ÷ 4 = 262

1048 ÷ 8 = 131

Therefore, the factors of 1048 are: 1, 2, 4, 8, 131, 262, 524, 1048.

Prime Factors and Prime Factorization

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

Using Prime Factorization: In this process, prime factors of 1048 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1048 ÷ 2 = 524

524 ÷ 2 = 262

262 ÷ 2 = 131

131 ÷ 131 = 1

The prime factors of 1048 are 2 and 131.

The prime factorization of 1048 is: 23 × 131.

Factor Tree

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

Step 1: Firstly, 1048 is divided by 2 to get 524.

Step 2: Now divide 524 by 2 to get 262.

Step 3: Then divide 262 by 2 to get 131

Step 4: Divide 131 by 131 to get 1. Here, 131 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1048 is: 23 × 131.

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 1048: (1, 1048), (2, 524), (4, 262), (8, 131).

Negative factor pairs of 1048: (-1, -1048), (-2, -524), (-4, -262), (-8, -131).

Common Mistakes and How to Avoid Them in Factors of 1048

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 8 teams and 1048 points to distribute equally. How many points will each team receive?

Okay, lets begin

Each team will receive 131 points.

Explanation

To distribute the points equally, we need to divide the total points by the number of teams.

1048/8 = 131

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 262 meters and the total area is 1048 square meters. Find the width?

Okay, lets begin

4 meters.

Explanation

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

Area = length × width

1048 = 262 × width

To find the value of width, we need to shift 262 to the left side.

1048/262 = width

Width = 4.

Well explained 👍

Problem 3

There are 524 packages and 1048 items. How many items will be in each package?

Okay, lets begin

Each package will have 2 items.

Explanation

To find the items in each package, divide the total items by the number of packages.

1048/524 = 2

Well explained 👍

Problem 4

In a seminar, there are 1048 participants, and they are divided into 4 groups. How many participants are there in each group?

Okay, lets begin

There are 262 participants in each group.

Explanation

Dividing the participants by the total groups, we will get the number of participants in each group.

1048/4 = 262

Well explained 👍

Problem 5

1048 books need to be arranged on 131 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 8 books.

Explanation

Divide total books by the number of shelves.

1048/131 = 8

Well explained 👍

FAQs on Factors of 1048

1.What are the factors of 1048?

1, 2, 4, 8, 131, 262, 524, 1048 are the factors of 1048.

2.Mention the prime factors of 1048.

The prime factors of 1048 are 2^3 × 131.

3.Is 1048 a multiple of 4?

4.Mention the factor pairs of 1048?

(1, 1048), (2, 524), (4, 262), (8, 131) are the factor pairs of 1048.

5.What is the square of 1048?

The square of 1048 is 1,098,304.

Important Glossaries for Factor of 1048

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1048 are 1, 2, 4, 8, 131, 262, 524, and 1048.
  • Prime factors: The factors which are prime numbers. For example, 2 and 131 are prime factors of 1048.
  • 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 1048 are (1, 1048), (2, 524), etc.
  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1048 is 23 × 131.
  • Multiplicative identity: The number 1 is the multiplicative identity because any number multiplied by 1 remains unchanged. For example, 1048 × 1 = 1048.

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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.