100 LearnersLast updated on May 26th, 2025
Factors of 1413
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 1413, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1413?
The numbers that divide 1413 evenly are known as factors of 1413.
A factor of 1413 is a number that divides the number without remainder.
The factors of 1413 are 1, 3, 11, 33, 43, 129, 473, and 1413.
Negative factors of 1413: -1, -3, -11, -33, -43, -129, -473, and -1413.
Prime factors of 1413: 3, 11, and 43.
Prime factorization of 1413: 3 × 11 × 43.
The sum of factors of 1413: 1 + 3 + 11 + 33 + 43 + 129 + 473 + 1413 = 2106
How to Find Factors of 1413?
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 1413. Identifying the numbers which are multiplied to get the number 1413 is the multiplication method.
Step 1: Multiply 1413 by 1, 1413 × 1 = 1413.
Step 2: Check for other numbers that give 1413 after multiplying
3 × 471 = 1413
11 × 129 = 1413
33 × 43 = 1413
Therefore, the positive factor pairs of 1413 are: (1, 1413), (3, 471), (11, 129), (33, 43).
All these factor pairs result in 1413.
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 1413 by 1, 1413 ÷ 1 = 1413.
Step 2: Continue dividing 1413 by the numbers until the remainder becomes 0.
1413 ÷ 1 = 1413
1413 ÷ 3 = 471
1413 ÷ 11 = 129
1413 ÷ 33 = 43
Therefore, the factors of 1413 are: 1, 3, 11, 33, 43, 129, 471, 1413.
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 1413 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1413 ÷ 3 = 471
471 ÷ 3 = 157
157 ÷ 11 = 14.27 (not a whole number, try the next prime number)
157 ÷ 43 = 3.65 (not a whole number, try the next prime number)
157 ÷ 157 = 1
The prime factors of 1413 are 3, 11, and 43.
The prime factorization of 1413 is: 3 × 11 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1413 is divided by 3 to get 471.
Step 2: Now divide 471 by 3 to get 157.
Step 3: Divide 157 by 11 but it doesn't result in an integer; try dividing by 43 but it doesn't result in an integer either.
Step 4: 157 is a prime number, divide it by itself to get 1.
So, the prime factorization of 1413 is: 3 × 11 × 43.
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 1413: (1, 1413), (3, 471), (11, 129), and (33, 43).
Negative factor pairs of 1413: (-1, -1413), (-3, -471), (-11, -129), and (-33, -43).
Common Mistakes and How to Avoid Them in Factors of 1413
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
People 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 1413, 1 and 1413 are also factors.
Factors of 1413 Examples
Problem 1
There are 3 teams and 1413 participants. How will they divide it equally?
Each team will have 471 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1413/3 = 471
Problem 2
A rectangular field has a width of 11 meters and a total area of 1413 square meters. Find the length.
129 meters.
Explanation
To find the length of the field, we use the formula,
Area = length × width
1413 = length × 11
To find the value of the length, we need to divide 1413 by 11.
1413/11 = length
Length = 129.
Problem 3
There are 129 boxes and 1413 items. How many items will be in each box?
Each box will have 11 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
1413/129 = 11
Problem 4
A class has 1413 students and 33 groups. How many students are there in each group?
There are 43 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1413/33 = 43
Problem 5
1413 books need to be arranged on 11 shelves. How many books will go on each shelf?
Each of the shelves has 129 books.
Explanation
Divide total books by shelves.
1413/11 = 129
FAQs on Factors of 1413
1.What are the factors of 1413?
2.Mention the prime factors of 1413.
3.Is 1413 a multiple of 3?
4.Mention the factor pairs of 1413?
5.What is the square of 1413?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1413?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1413 with numbers?
8.What role do numbers and Factors of 1413 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 1413 skills?
Important Glossaries for Factor of 1413
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1413 are 1, 3, 11, 33, 43, 129, 471, and 1413.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 43 are prime factors of 1413.
- 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 1413 are (1, 1413), (3, 471), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1413 is 3 × 11 × 43.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply together to give the original number.
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About BrightChamps in United Arab Emirates
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.
