Factors of 1424
2026-02-28 23:53 Diff
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Last updated on December 15, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1424, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 1424?

The numbers that divide 1424 evenly are known as factors of 1424.

A factor of 1424 is a number that divides the number without remainder.

The factors of 1424 are 1, 2, 4, 8, 16, 89, 178, 356, 712, and 1424.

Negative factors of 1424: -1, -2, -4, -8, -16, -89, -178, -356, -712, and -1424.

Prime factors of 1424: 2 and 89.

Prime factorization of 1424: 24 × 89.

The sum of factors of 1424: 1 + 2 + 4 + 8 + 16 + 89 + 178 + 356 + 712 + 1424 = 2790

How to Find Factors of 1424?

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 1424. Identifying the numbers which are multiplied to get the number 1424 is the multiplication method.

Step 1: Multiply 1424 by 1, 1424 × 1 = 1424.

Step 2: Check for other numbers that give 1424 after multiplying     

2 × 712 = 1424    

 4 × 356 = 1424     

8 × 178 = 1424     

16 × 89 = 1424

Therefore, the positive factor pairs of 1424 are: (1, 1424), (2, 712), (4, 356), (8, 178), (16, 89).

All these factor pairs result in 1424.

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 1424 by 1, 1424 ÷ 1 = 1424.

Step 2: Continue dividing 1424 by the numbers until the remainder becomes 0.

1424 ÷ 1 = 1424

1424 ÷ 2 = 712

1424 ÷ 4 = 356

1424 ÷ 8 = 178

1424 ÷ 16 = 89

Therefore, the factors of 1424 are: 1, 2, 4, 8, 16, 89, 178, 356, 712, 1424.

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: In this process, prime factors of 1424 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1424 ÷ 2 = 712

712 ÷ 2 = 356

356 ÷ 2 = 178

178 ÷ 2 = 89

89 ÷ 89 = 1

The prime factors of 1424 are 2 and 89.

The prime factorization of 1424 is: 24 × 89.

Factor Tree

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

Step 1: Firstly, 1424 is divided by 2 to get 712.

Step 2: Now divide 712 by 2 to get 356.

Step 3: Then divide 356 by 2 to get 178.

Step 4: Divide 178 by 2 to get 89. Here, 89 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 1424 is: 24 × 89.

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 1424: (1, 1424), (2, 712), (4, 356), (8, 178), and (16, 89).

Negative factor pairs of 1424: (-1, -1424), (-2, -712), (-4, -356), (-8, -178), and (-16, -89).

Common Mistakes and How to Avoid Them in Factors of 1424

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

A group of 4 friends plans to share 1424 candies equally. How many candies will each friend get?

Okay, lets begin

Each friend will get 356 candies.

Explanation

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

1424/4 = 356

Well explained 👍

Problem 2

A rectangular garden has a length of 16 meters and an area of 1424 square meters. Find the width of the garden.

Okay, lets begin

89 meters.

Explanation

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

 Area = length × width     

1424 = 16 × width     

To find the value of width, we need to shift 16 to the left side.    

 1424/16 = width     

Width = 89.

Well explained 👍

Problem 3

There are 8 storage boxes and 1424 items. How many items will be in each box?

Okay, lets begin

Each box will have 178 items.

Explanation

To find the items in each box, divide the total items by the boxes.     

1424/8 = 178

Well explained 👍

Problem 4

In a company, there are 178 employees and each team consists of 8 people. How many teams can be formed?

Okay, lets begin

22 teams.

Explanation

Dividing the employees by the team size, we will get the number of teams.     178/8 = 22

Well explained 👍

Problem 5

A library has 1424 books that need to be placed in 8 shelves. How many books will go on each shelf?

Okay, lets begin

Each shelf will have 178 books.

Explanation

Divide total books by shelves.    

 1424/8 = 178

Well explained 👍

FAQs on Factors of 1424

1.What are the factors of 1424?

1, 2, 4, 8, 16, 89, 178, 356, 712, 1424 are the factors of 1424.

2.Mention the prime factors of 1424.

The prime factors of 1424 are 24 × 89.

3.Is 1424 a multiple of 16?

4.Mention the factor pairs of 1424?

(1, 1424), (2, 712), (4, 356), (8, 178), and (16, 89) are the factor pairs of 1424.

5.What is the square of 1424?

The square of 1424 is 2027776.

Important Glossaries for Factors of 1424

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1424 are 1, 2, 4, 8, 16, 89, 178, 356, 712, and 1424.
  • Prime factors: The factors which are prime numbers. For example, 2 and 89 are prime factors of 1424.
  • 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 1424 are (1, 1424), (2, 712), etc.
  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1424 is 24 × 89.
  • Negative factors: Factors that are negative can be derived from the positive factors. For example, -1, -2, -4, etc., are negative factors of 1424.

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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.