127 LearnersLast updated on May 26th, 2025
Factors of 1406
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 1406, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1406?
The numbers that divide 1406 evenly are known as factors of 1406.
A factor of 1406 is a number that divides the number without remainder.
The factors of 1406 are 1, 2, 703, and 1406.
Negative factors of 1406: -1, -2, -703, and -1406.
Prime factors of 1406: 2 and 703.
Prime factorization of 1406: 2 × 703.
The sum of factors of 1406: 1 + 2 + 703 + 1406 = 2112
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How to Find Factors of 1406?
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 1406. Identifying the numbers which are multiplied to get the number 1406 is the multiplication method.
Step 1: Multiply 1406 by 1, 1406 × 1 = 1406.
Step 2: Check for other numbers that give 1406 after multiplying
2 × 703 = 1406
Therefore, the positive factor pairs of 1406 are: (1, 1406) and (2, 703).
All these factor pairs result in 1406.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1406 by 1, 1406 ÷ 1 = 1406.
Step 2: Continue dividing 1406 by the numbers until the remainder becomes 0.
1406 ÷ 1 = 1406
1406 ÷ 2 = 703
Therefore, the factors of 1406 are: 1, 2, 703, 1406.
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 1406 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1406 ÷ 2 = 703
703 is a prime number and cannot be divided further.
The prime factors of 1406 are 2 and 703.
The prime factorization of 1406 is: 2 × 703.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1406 is divided by 2 to get 703. 703 is a prime number, so it cannot be divided further.
So, the prime factorization of 1406 is: 2 × 703.
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 1406: (1, 1406) and (2, 703).
Negative factor pairs of 1406: (-1, -1406) and (-2, -703).
Common Mistakes and How to Avoid Them in Factors of 1406
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 1406, 1 and 1406 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 1406 consist of -1, -2, -703, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1406/1.5 = 937.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1406 are prime numbers.
For example, 2 and 703 are the prime factors of 1406, but it has other factors like 1 and 1406.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1406 as 2 × 703 and missing all the key factors.
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Factors of 1406 Examples
Problem 1
There are 14 students and 1406 pages of a book. How will they share it equally?
They will get 100 pages each.
Explanation
To divide the pages equally, we need to divide the total pages with the number of students.
1406/14 = 100.
428 Since we need whole numbers, each student will get 100 pages, and the remainder will be 6 pages.
Problem 2
A rectangular garden has a length of 703 meters and a total area of 1406 square meters. Find the width?
2 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1406 = 703 × width
To find the value of width, we need to shift 703 to the left side.
1406/703 = width
Width = 2.
Problem 3
There are 2 containers and 1406 marbles. How many marbles will be in each container?
Each container will have 703 marbles.
Explanation
To find the marbles in each container, divide the total marbles with the containers.
1406/2 = 703
Problem 4
In a class, there are 703 students, and 2 teams. How many students are there in each team?
There are 351 students in each team.
Explanation
Dividing the students with the total teams, we will get the number of students in each team.
703/2 = 351.5
Since we need whole numbers, each team will get 351 students, and the remainder will be 1 student.
Problem 5
1406 books need to be arranged in 703 shelves. How many books will go on each shelf?
Each of the shelves has 2 books.
Explanation
Divide total books with shelves.
1406/703 = 2
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FAQs on Factors of 1406
1.What are the factors of 1406?
2.Mention the prime factors of 1406.
3.Is 1406 a multiple of 2?
4.Mention the factor pairs of 1406?
5.What is the square of 1406?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1406?
7.What are some fun ways kids in Qatar can practice Factors of 1406 with numbers?
8.What role do numbers and Factors of 1406 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1406 skills?
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Important Glossaries for Factor of 1406
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1406 are 1, 2, 703, and 1406.
- Prime factors: The factors which are prime numbers. For example, 2 and 703 are prime factors of 1406.
- 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 1406 are (1, 1406) and (2, 703).
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1406 is 2 × 703.
- Multiple: A number that can be divided by another number without a remainder. For example, 1406 is a multiple of 2.
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About BrightChamps in Qatar
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.
