101 LearnersLast updated on May 26th, 2025
Factors of 402
Factors are the numbers that divide any given number evenly without a 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 402, how they are used in real life, and tips to learn them quickly.
What are the Factors of 402?
The numbers that divide 402 evenly are known as factors of 402.
A factor of 402 is a number that divides the number without a remainder.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, and 402.
Negative factors of 402: -1, -2, -3, -6, -67, -134, -201, and -402.
Prime factors of 402: 2, 3, and 67.
Prime factorization of 402: 2 × 3 × 67.
The sum of factors of 402: 1 + 2 + 3 + 6 + 67 + 134 + 201 + 402 = 816
How to Find Factors of 402?
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 402. Identifying the numbers that are multiplied to get the number 402 is the multiplication method.
Step 1: Multiply 402 by 1, 402 × 1 = 402.
Step 2: Check for other numbers that give 402 after multiplying
2 × 201 = 402
3 × 134 = 402
6 × 67 = 402
Therefore, the positive factor pairs of 402 are: (1, 402), (2, 201), (3, 134), (6, 67).
All these factor pairs result in 402.
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 402 by 1, 402 ÷ 1 = 402.
Step 2: Continue dividing 402 by the numbers until the remainder becomes 0.
402 ÷ 1 = 40
2 402 ÷ 2 = 201
402 ÷ 3 = 134
402 ÷ 6 = 67
Therefore, the factors of 402 are: 1, 2, 3, 6, 67, 134, 201, 402.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 402 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
402 ÷ 2 = 201
201 ÷ 3 = 67
67 ÷ 67 = 1
The prime factors of 402 are 2, 3, and 67.
The prime factorization of 402 is: 2 × 3 × 67.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 402 is divided by 2 to get 201.
Step 2: Now divide 201 by 3 to get 67.
Step 3: Divide 67 by 67 to get 1. Here, 67 is a prime number, which cannot be divided anymore.
So, the prime factorization of 402 is: 2 × 3 × 67.
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 402: (1, 402), (2, 201), (3, 134), (6, 67).
Negative factor pairs of 402: (-1, -402), (-2, -201), (-3, -134), (-6, -67).
Common Mistakes and How to Avoid Them in Factors of 402
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 402, 1 and 402 is also a factor.
Factors of 402 Examples
Problem 1
There are 6 teams and 402 participants. How will they divide equally?
They will have 67 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
402/6 = 67
Problem 2
A garden is rectangular, the length of the garden is 134 meters, and the total area is 402 square meters. Find the width?
3 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 402 = 134 × width
To find the value of width, we need to shift 134 to the left side.
402/134 = width
Width = 3.
Problem 3
There are 3 boxes and 402 oranges. How many oranges will be in each box?
Each box will have 134 oranges.
Explanation
To find the oranges in each box, divide the total oranges by the number of boxes.
402/3 = 134
Problem 4
In a conference, there are 402 attendees, and 2 rooms. How many attendees are there in each room?
There are 201 attendees in each room.
Explanation
Dividing the attendees by the total rooms, we will get the number of attendees in each room.
402/2 = 201
Problem 5
402 people need to be seated in 67 rows. How many people will be in each row?
Each row has 6 people.
Explanation
Divide the total people by the rows.
402/67 = 6
FAQs on Factors of 402
1.What are the factors of 402?
2.Mention the prime factors of 402.
3.Is 402 a multiple of 3?
4.Mention the factor pairs of 402?
5.What is the square of 402?
6.How can children in India use numbers in everyday life to understand Factors of 402?
7.What are some fun ways kids in India can practice Factors of 402 with numbers?
8.What role do numbers and Factors of 402 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 402 skills?
Important Glossaries for Factors of 402
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 402 are 1, 2, 3, 6, 67, 134, 201, and 402.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 67 are prime factors of 402.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 402 is 2 × 3 × 67.
- 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 402 are (1, 402), (2, 201), etc.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the number. For example, 2 × 201 = 402.
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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.
