118 LearnersLast updated on May 26th, 2025
Factors of 706
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 706, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 706?
The numbers that divide 706 evenly are known as factors of 706.
A factor of 706 is a number that divides the number without remainder.
The factors of 706 are 1, 2, 353, and 706.
Negative factors of 706: -1, -2, -353, and -706.
Prime factors of 706: 2 and 353.
Prime factorization of 706: 2 × 353.
The sum of factors of 706: 1 + 2 + 353 + 706 = 1062
How to Find Factors of 706?
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 706. Identifying the numbers which are multiplied to get the number 706 is the multiplication method.
Step 1: Multiply 706 by 1, 706 × 1 = 706.
Step 2: Check for other numbers that give 706 after multiplying 2 × 353 = 706
Therefore, the positive factor pairs of 706 are: (1, 706), (2, 353).
All these factor pairs result in 706.
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 706 by 1, 706 ÷ 1 = 706.
Step 2: Continue dividing 706 by the numbers until the remainder becomes 0.
706 ÷ 1 = 706
706 ÷ 2 = 353
Therefore, the factors of 706 are: 1, 2, 353, 706.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 706 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
706 ÷ 2 = 353
353 ÷ 353 = 1
The prime factors of 706 are 2 and 353.
The prime factorization of 706 is: 2 × 353.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 706 is divided by 2 to get 353.
Step 2: Here, 353 is a prime number, so the division stops. So, the prime factorization of 706 is: 2 × 353.
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 706: (1, 706), (2, 353).
Negative factor pairs of 706: (-1, -706), (-2, -353).
Common Mistakes and How to Avoid Them in Factors of 706
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 706, 1 and 706 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 706 consist of -1, -2, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 706/1.5 = 470.666, 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 706 are prime numbers.
For example, 2 and 353 are the prime factors of 706, but it has other factors like 1, 706.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 706 as 2 × 353 and missing all the key factors.
Factors of 706 Examples
Problem 1
There are 353 students at an event and 706 chairs. How will they divide the chairs equally?
Each student will get 2 chairs.
Explanation
To divide the chairs equally, we need to divide the total chairs by the number of students.
706/353 = 2
Problem 2
A rectangular garden has a length of 353 meters and a total area of 706 square meters. Find the width.
2 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
706 = 353 × width
To find the value of width, we need to shift 353 to the left side.
706/353 = width
Width = 2.
Problem 3
There are 2 teams and 706 points. How many points will each team get if divided equally?
Each team will have 353 points.
Explanation
To find the points for each team, divide the total points by the number of teams.
706/2 = 353
Problem 4
In a classroom, there are 706 pencils and 353 students. How many pencils will each student get?
Each student will get 2 pencils.
Explanation
Dividing the pencils by the number of students, we will get the number of pencils each student receives.
706/353 = 2
Problem 5
706 bricks need to be stacked in 353 piles. How many bricks will go in each pile?
Each pile will have 2 bricks.
Explanation
Divide total bricks by the number of piles.
706/353 = 2
FAQs on Factors of 706
1.What are the factors of 706?
2.Mention the prime factors of 706.
3.Is 706 a multiple of 2?
4.Mention the factor pairs of 706?
5.What is the square of 706?
6.How can children in United States use numbers in everyday life to understand Factors of 706?
7.What are some fun ways kids in United States can practice Factors of 706 with numbers?
8.What role do numbers and Factors of 706 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 706 skills?
Important Glossaries for Factor of 706
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 706 are 1, 2, 353, and 706.
- Prime factors: The factors which are prime numbers. For example, 2 and 353 are prime factors of 706.
- 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 706 are (1, 706) and (2, 353).
- Prime factorization: The process of expressing a number as the product of its prime factors. For 706, it is 2 × 353.
- Division method: A technique to find factors by dividing the number with whole numbers until the remainder is zero.
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About BrightChamps in United States
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.
