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Last updated on May 26th, 2025

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Factors of 1408

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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 1408, how they are used in real life, and the tips to learn them quickly.

Factors of 1408 for Bahraini Students
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What are the Factors of 1408?

The numbers that divide 1408 evenly are known as factors of 1408.

 

A factor of 1408 is a number that divides the number without remainder.

 

The factors of 1408 are 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, and 1408.

 

Negative factors of 1408: -1, -2, -4, -8, -16, -32, -44, -88, -176, -352, -704, and -1408.

 

Prime factors of 1408: 2 and 11.

 

Prime factorization of 1408: 26 × 11.

 

The sum of factors of 1408: 1 + 2 + 4 + 8 + 16 + 32 + 44 + 88 + 176 + 352 + 704 + 1408 = 2835

factors of 1408

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How to Find Factors of 1408?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1408. Identifying the numbers which are multiplied to get the number 1408 is the multiplication method.

 

Step 1: Multiply 1408 by 1, 1408 × 1 = 1408.

 

Step 2: Check for other numbers that give 1408 after multiplying

2 × 704 = 1408

4 × 352 = 1408

8 × 176 = 1408

16 × 88 = 1408

32 × 44 = 1408

 

Therefore, the positive factor pairs of 1408 are: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), (32, 44).

 

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 1408 by 1, 1408 ÷ 1 = 1408.

 

Step 2: Continue dividing 1408 by the numbers until the remainder becomes 0.

1408 ÷ 1 = 1408

1408 ÷ 2 = 704

1408 ÷ 4 = 352

1408 ÷ 8 = 176

1408 ÷ 16 = 88

1408 ÷ 32 = 44

 

Therefore, the factors of 1408 are: 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, 1408.

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Prime Factors and Prime Factorization

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

  • Using prime factorization
  • Using factor tree

 

Using Prime Factorization: In this process, prime factors of 1408 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1408 ÷ 2 = 704

704 ÷ 2 = 352

352 ÷ 2 = 176

176 ÷ 2 = 88

88 ÷ 2 = 44

44 ÷ 2 = 22

22 ÷ 2 = 11

11 ÷ 11 = 1

 

The prime factors of 1408 are 2 and 11. The prime factorization of 1408 is: 26 × 11.

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Factor Tree

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

 

Step 1: Firstly, 1408 is divided by 2 to get 704.

 

Step 2: Now divide 704 by 2 to get 352.

 

Step 3: Then divide 352 by 2 to get 176.

 

Step 4: Continue dividing by 2 until you get 11.

 

Step 5: Finally divide 11 by 11 to get 1. Here, 11 is the smallest prime number that cannot be divided anymore.

 

So, the prime factorization of 1408 is: 26 × 11.

 

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 1408: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), and (32, 44).

 

Negative factor pairs of 1408: (-1, -1408), (-2, -704), (-4, -352), (-8, -176), (-16, -88), and (-32, -44).

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Common Mistakes and How to Avoid Them in Factors of 1408

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

Mistake 1

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 1408, 1 and 1408 are also factors.

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Factors of 1408 Examples

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Problem 1

There are 16 friends and 1408 candies. How will they divide it equally?

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They will get 88 candies each.

Explanation

To divide the candies equally, we need to divide the total candies by the number of friends.

1408/16 = 88

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Problem 2

A field is rectangular, and the length of the field is 88 meters. The total area is 1408 square meters. Find the width.

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16 meters.

Explanation

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

Area = length × width

1408 = 88 × width

To find the value of width, we need to shift 88 to the left side.

1408/88 = width

Width = 16.

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Problem 3

There are 32 bags and 1408 apples. How many apples will be in each bag?

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Each bag will have 44 apples.

Explanation

To find the apples in each bag, divide the total apples by the bags.

1408/32 = 44

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Problem 4

In a school, there are 1408 students, and 44 classes. How many students are there in each class?

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There are 32 students in each class.

Explanation

Dividing the students by the total classes, we will get the number of students in each class.

1408/44 = 32

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Problem 5

1408 books need to be arranged in 88 shelves. How many books will go on each shelf?

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Each of the shelves has 16 books.

Explanation

Divide total books by shelves.

1408/88 = 16

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FAQs on Factors of 1408

1.What are the factors of 1408?

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2.Mention the prime factors of 1408.

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3.Is 1408 a multiple of 4?

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4.Mention the factor pairs of 1408?

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5.What is the square of 1408?

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6.How can children in Bahrain use numbers in everyday life to understand Factors of 1408?

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7.What are some fun ways kids in Bahrain can practice Factors of 1408 with numbers?

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8.What role do numbers and Factors of 1408 play in helping children in Bahrain develop problem-solving skills?

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9.How can families in Bahrain create number-rich environments to improve Factors of 1408 skills?

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Important Glossaries for Factor of 1408

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1408 are 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, and 1408.

 

  • Prime factors: The factors which are prime numbers. For example, 2 and 11 are prime factors of 1408.

 

  • 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 1408 are (1, 1408), (2, 704), etc.

 

  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1408 is 26 × 11.

 

  • Multiple: The result of multiplying a number by an integer. For example, 1408 is a multiple of 4.
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About BrightChamps in Bahrain

At BrightChamps, numbers are more than just digits—they unlock countless opportunities! Our goal is to help kids all over Bahrain build essential math skills, focusing today on Factors of 1408 with a special focus on factors—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Wahooo! Waterpark, keeping track of local football scores, or managing their allowance for gadgets, mastering numbers boosts everyday confidence. Our interactive lessons make learning simple and enjoyable. Since kids in Bahrain learn in various ways, we adapt lessons to fit each learner. From Manama’s lively city to peaceful beaches, BrightChamps brings math to life all over Bahrain. Let’s make factors a fun part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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