100 LearnersLast updated on May 26th, 2025
Factors of 1706
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 1706, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1706?
The numbers that divide 1706 evenly are known as factors of 1706.
A factor of 1706 is a number that divides the number without a remainder.
The factors of 1706 are 1, 2, 11, 22, 77, 154, 853, and 1706.
Negative factors of 1706: -1, -2, -11, -22, -77, -154, -853, and -1706.
Prime factors of 1706: 2 and 11, and 853 (since 853 is a prime number).
Prime factorization of 1706: 2 × 11 × 853.
The sum of factors of 1706: 1 + 2 + 11 + 22 + 77 + 154 + 853 + 1706 = 2826
How to Find Factors of 1706?
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 1706. Identifying the numbers which are multiplied to get the number 1706 is the multiplication method.
Step 1: Multiply 1706 by 1, 1706 × 1 = 1706.
Step 2: Check for other numbers that give 1706 after multiplying
2 × 853 = 1706
11 × 154 = 1706
22 × 77 = 1706
Therefore, the positive factor pairs of 1706 are: (1, 1706), (2, 853), (11, 154), (22, 77).
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 the simple division method
Step 1: Divide 1706 by 1, 1706 ÷ 1 = 1706.
Step 2: Continue dividing 1706 by the numbers until the remainder becomes 0.
1706 ÷ 1 = 1706
1706 ÷ 2 = 853
1706 ÷ 11 = 154
1706 ÷ 22 = 77
Therefore, the factors of 1706 are: 1, 2, 11, 22, 77, 154, 853, and 1706.
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 1706 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1706 ÷ 2 = 853
853 is a prime number, so it cannot be divided further by any number other than itself and 1.
The prime factors of 1706 are 2, 11, and 853.
The prime factorization of 1706 is: 2 × 11 × 853.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1706 is divided by 2 to get 853.
Step 2: 853 is a prime number and cannot be divided further. So, the prime factorization of 1706 is: 2 × 11 × 853.
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 1706: (1, 1706), (2, 853), (11, 154), and (22, 77).
Negative factor pairs of 1706: (-1, -1706), (-2, -853), (-11, -154), and (-22, -77).
Common Mistakes and How to Avoid Them in Factors of 1706
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 1706, 1 and 1706 are also factors.
Factors of 1706 Examples
Problem 1
There are 17 friends and 1706 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1706/17 = 100
Problem 2
A rectangular plot of land has a length of 11 meters and a total area of 1706 square meters. Find the width.
154 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1706 = 11 × width
To find the value of width, we need to shift 11 to the left side.
1706/11 = width
Width = 154.
Problem 3
There are 22 boxes and 1706 marbles. How many marbles will be in each box?
Each box will have 77 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
1706/22 = 77
Problem 4
In a classroom, there are 1706 students, and 154 groups. How many students are there in each group?
There are 11 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1706/154 = 11
Problem 5
1706 books need to be arranged in 853 shelves. How many books will go on each shelf?
Each of the shelves has 2 books.
Explanation
Divide total books by shelves.
1706/853 = 2
FAQs on Factors of 1706
1.What are the factors of 1706?
2.Mention the prime factors of 1706.
3.Is 1706 a multiple of 11?
4.Mention the factor pairs of 1706?
5.What is the square of 1706?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1706?
7.What are some fun ways kids in Qatar can practice Factors of 1706 with numbers?
8.What role do numbers and Factors of 1706 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1706 skills?
Important Glossaries for Factor of 1706
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1706 are 1, 2, 11, 22, 77, 154, 853, and 1706.
- Prime factors: The factors which are prime numbers. For example, 2, 11, and 853 are prime factors of 1706.
- 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 1706 are (1, 1706), (2, 853), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1706 is 2 × 11 × 853.
- Multiples: Numbers that can be obtained by multiplying a given number by integers. For example, 1706 is a multiple of 1, 2, 11, etc.
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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.
