102 LearnersLast updated on May 26th, 2025
Factors of 429
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.
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
- Using factor tree
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.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 429, 1 and 429 are also factors.
Factors of 429 Examples
Problem 1
There are 3 teams and 429 players. How will the players be divided equally among the teams?
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
Problem 2
An auditorium can accommodate 429 chairs arranged in 11 rows. How many chairs are there in each row?
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
Problem 3
A library has 13 shelves and 429 books. How many books will be on each shelf?
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
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?
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
Problem 5
429 apples need to be packed into boxes with each box containing 13 apples. How many boxes will be needed?
33 boxes are needed.
Explanation
Divide the total apples by the number of apples per box.
429/13 = 33
FAQs on Factors of 429
1.What are the factors of 429?
2.Mention the prime factors of 429.
3.Is 429 a multiple of 13?
4.Mention the factor pairs of 429?
5.What is the square of 429?
6.How can children in Canada use numbers in everyday life to understand Factors of 429?
7.What are some fun ways kids in Canada can practice Factors of 429 with numbers?
8.What role do numbers and Factors of 429 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 429 skills?
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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About BrightChamps in Canada
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.
