140 LearnersLast updated on May 26th, 2025
Factors of 1806
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 1806, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1806?
The numbers that divide 1806 evenly are known as factors of 1806.
A factor of 1806 is a number that divides the number without remainder.
The factors of 1806 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 54, 69, 78, 117, 138, 234, 261, 391, 522, 783, and 1806.
Negative factors of 1806: -1, -2, -3, -6, -9, -13, -18, -26, -39, -54, -69, -78, -117, -138, -234, -261, -391, -522, -783, and -1806.
Prime factors of 1806: 2, 3, and 13.
Prime factorization of 1806: 2 × 3^2 × 13^2.
The sum of factors of 1806: 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 39 + 54 + 69 + 78 + 117 + 138 + 234 + 261 + 391 + 522 + 783 + 1806 = 4572
How to Find Factors of 1806?
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 1806. Identifying the numbers which are multiplied to get the number 1806 is the multiplication method.
Step 1: Multiply 1806 by 1, 1806 × 1 = 1806.
Step 2: Check for other numbers that give 1806 after multiplying
2 × 903 = 1806
3 × 602 = 1806
6 × 301 = 1806
9 × 201 = 1806
13 × 139 = 1806
Therefore, the positive factor pairs of 1806 are: (1, 1806), (2, 903), (3, 602), (6, 301), (9, 201), (13, 139).
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 1806 by 1, 1806 ÷ 1 = 1806.
Step 2: Continue dividing 1806 by numbers until the remainder becomes 0.
1806 ÷ 1 = 1806
1806 ÷ 2 = 903
1806 ÷ 3 = 602
1806 ÷ 6 = 301
1806 ÷ 9 = 201
1806 ÷ 13 = 139
Therefore, the factors of 1806 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 54, 69, 78, 117, 138, 234, 261, 391, 522, 783, and 1806.
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 1806 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1806 ÷ 2 = 903
903 ÷ 3 = 301
301 ÷ 13 = 23
23 ÷ 23 = 1
The prime factors of 1806 are 2, 3, and 13.
The prime factorization of 1806 is: 2 × 3^2 × 13^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1806 is divided by 2 to get 903.
Step 2: Now divide 903 by 3 to get 301.
Step 3: Then divide 301 by 13 to get 23.
Here, 23 is a prime number that cannot be divided anymore.
So, the prime factorization of 1806 is: 2 × 3^2 × 13^2.
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 1806: (1, 1806), (2, 903), (3, 602), (6, 301), (9, 201), (13, 139).
Negative factor pairs of 1806: (-1, -1806), (-2, -903), (-3, -602), (-6, -301), (-9, -201), (-13, -139).
Common Mistakes and How to Avoid Them in Factors of 1806
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 1806, 1 and 1806 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1806 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1806/1.5 = 1204, 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 1806 are prime numbers. 2, 3, and 13 are the prime factors of 1806, but it has other factors like 6, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 1806 as 2 × 3^2 × 13^2 and missing key factors.
Factors of 1806 Examples
Problem 1
There are 6 teams and 1806 sports equipment pieces. How will they distribute them equally?
They will get 301 pieces each.
Explanation
To divide the equipment equally, we need to divide the total pieces by the number of teams.
1806/6 = 301
Problem 2
A farm is rectangular, with the length of the farm being 18 meters and the total area being 1806 square meters. Find the width?
The width is 100.333 meters.
Explanation
To find the width of the farm, we use the formula,
Area = length × width
1806 = 18 × width
To find the value of width, divide 1806 by 18.
1806/18 = 100.333
Problem 3
There are 9 boxes and 1806 marbles. How many marbles will be in each box?
Each box will have 201 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1806/9 = 201
Problem 4
In an event, there are 13 stations and 1806 participants. How many participants are there at each station?
There are 139 participants at each station.
Explanation
Dividing the participants by the total stations, we will get the number of participants at each station.
1806/13 = 139
Problem 5
1806 tulip bulbs need to be planted in 3 gardens. How many bulbs will go in each garden?
Each garden will have 602 bulbs.
Explanation
Divide the total bulbs by the number of gardens.
1806/3 = 602
FAQs on Factors of 1806
1.What are the factors of 1806?
2.Mention the prime factors of 1806.
3.Is 1806 a multiple of 9?
4.Mention the factor pairs of 1806?
5.What is the square of 1806?
6.How can children in Canada use numbers in everyday life to understand Factors of 1806?
7.What are some fun ways kids in Canada can practice Factors of 1806 with numbers?
8.What role do numbers and Factors of 1806 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1806 skills?
Important Glossaries for Factors of 1806
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1806 are 1, 2, 3, 6, 9, 13, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 1806.
- Factor pairs: Two numbers in a pair that multiply to give the original number are called factor pairs. For example, the factor pairs of 1806 are (1, 1806), (2, 903), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For 1806, it's 2 × 3^2 × 13^2.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 1806 is a multiple of 9.
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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.
