Factors of 429
2026-02-28 11:08 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 429, how they are used in real life, and tips to learn them quickly.

What are the Factors of 429?

The numbers that divide 429 evenly are known as factors of 429.

A factor of 429 is a number that divides the number without remainder.

The factors of 429 are 1, 3, 11, 13, 33, 39, 143, and 429.

Negative factors of 429: -1, -3, -11, -13, -33, -39, -143, and -429.

Prime factors of 429: 3, 11, and 13.

Prime factorization of 429: 3 × 11 × 13.

The sum of factors of 429: 1 + 3 + 11 + 13 + 33 + 39 + 143 + 429 = 672

How to Find Factors of 429?

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

  • Finding factors using multiplication
     
  • Finding factors using the 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 429. Identifying the numbers that are multiplied to get the number 429 is the multiplication method.

Step 1: Multiply 429 by 1, 429 × 1 = 429.

Step 2: Check for other numbers that give 429 after multiplying

3 × 143 = 429

11 × 39 = 429

13 × 33 = 429

Therefore, the positive factor pairs of 429 are: (1, 429), (3, 143), (11, 39), (13, 33).

All these factor pairs result in 429. 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 429 by 1, 429 ÷ 1 = 429.

Step 2: Continue dividing 429 by the numbers until the remainder becomes 0.

429 ÷ 1 = 429

429 ÷ 3 = 143

429 ÷ 11 = 39

429 ÷ 13 = 33

Therefore, the factors of 429 are: 1, 3, 11, 13, 33, 39, 143, 429.

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 429 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

429 ÷ 3 = 143

143 ÷ 11 = 13

13 ÷ 13 = 1

The prime factors of 429 are 3, 11, and 13.

The prime factorization of 429 is: 3 × 11 × 13.

Factor Tree

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

Step 1: Firstly, 429 is divided by 3 to get 143.

Step 2: Now divide 143 by 11 to get 13. Step 3: 13 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 429 is: 3 × 11 × 13.

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 429: (1, 429), (3, 143), (11, 39), (13, 33).

Negative factor pairs of 429: (-1, -429), (-3, -143), (-11, -39), (-13, -33).

Common Mistakes and How to Avoid Them in Factors of 429

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 3 teams and 429 players. How will the players be divided equally among the teams?

Okay, lets begin

Each team will have 143 players.

Explanation

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

429/3 = 143

Well explained 👍

Problem 2

An auditorium can accommodate 429 chairs arranged in 11 rows. How many chairs are there in each row?

Okay, lets begin

39 chairs.

Explanation

To find the number of chairs in each row, we use the formula,

Total chairs = rows × chairs per row

429 = 11 × chairs per row

To find the value of chairs per row, we need to divide 429 by 11.

429/11 = 39

Well explained 👍

Problem 3

A library has 13 shelves and 429 books. How many books will be on each shelf?

Okay, lets begin

Each shelf will have 33 books.

Explanation

To find the books in each shelf, divide the total books by the number of shelves.

429/13 = 33

Well explained 👍

Problem 4

In a class, there are 429 students, and they need to form groups of 11. How many students will be in each group?

Okay, lets begin

There are 39 students in each group.

Explanation

Dividing the students by the group size, we will get the number of students in each group.

429/11 = 39

Well explained 👍

Problem 5

429 apples need to be packed into boxes with each box containing 13 apples. How many boxes will be needed?

Okay, lets begin

33 boxes are needed.

Explanation

Divide the total apples by the number of apples per box.

429/13 = 33

Well explained 👍

FAQs on Factors of 429

1.What are the factors of 429?

1, 3, 11, 13, 33, 39, 143, 429 are the factors of 429.

2.Mention the prime factors of 429.

The prime factors of 429 are 3 × 11 × 13.

3.Is 429 a multiple of 13?

4.Mention the factor pairs of 429?

(1, 429), (3, 143), (11, 39), and (13, 33) are the factor pairs of 429.

5.What is the square of 429?

Important Glossaries for Factor of 429

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 429 are 1, 3, 11, 13, 33, 39, 143, and 429.
     
  • Prime factors: The factors which are prime numbers. For example, 3, 11, and 13 are prime factors of 429.
     
  • 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 429 are (1, 429), (3, 143), etc.
     
  • Prime factorization: The expression of a number as the product of its prime factors. For 429, it is 3 × 11 × 13.
     
  • Multiples: The result of multiplying a number by an integer. For instance, 429 is a multiple of 3, 11, and 13.

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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.