125 LearnersLast updated on May 26th, 2025
Factors of 710
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 710, how they are used in real life, and tips to learn them quickly.
What are the Factors of 710?
The numbers that divide 710 evenly are known as factors of 710.
A factor of 710 is a number that divides the number without remainder.
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, and 710.
Negative factors of 710: -1, -2, -5, -10, -71, -142, -355, and -710.
Prime factors of 710: 2, 5, and 71.
Prime factorization of 710: 2 × 5 × 71.
The sum of factors of 710: 1 + 2 + 5 + 10 + 71 + 142 + 355 + 710 = 1296
How to Find Factors of 710?
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 710. Identifying the numbers which are multiplied to get the number 710 is the multiplication method.
Step 1: Multiply 710 by 1, 710 × 1 = 710.
Step 2: Check for other numbers that give 710 after multiplying
2 × 355 = 710
5 × 142 = 710
10 × 71 = 710
Therefore, the positive factor pairs of 710 are: (1, 710), (2, 355), (5, 142), (10, 71).
All these factor pairs result in 710. 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 710 by 1, 710 ÷ 1 = 710.
Step 2: Continue dividing 710 by the numbers until the remainder becomes 0.
710 ÷ 1 = 710
710 ÷ 2 = 355
710 ÷ 5 = 142
710 ÷ 10 = 71
Therefore, the factors of 710 are: 1, 2, 5, 10, 71, 142, 355, 710.
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 710 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
710 ÷ 2 = 355
355 ÷ 5 = 71
71 ÷ 71 = 1
The prime factors of 710 are 2, 5, and 71.
The prime factorization of 710 is: 2 × 5 × 71.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 710 is divided by 2 to get 355.
Step 2: Now divide 355 by 5 to get 71.
Step 3: 71 is a prime number and cannot be divided anymore.
So, the prime factorization of 710 is: 2 × 5 × 71.
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 710: (1, 710), (2, 355), (5, 142), and (10, 71).
Negative factor pairs of 710: (-1, -710), (-2, -355), (-5, -142), and (-10, -71).
Common Mistakes and How to Avoid Them in Factors of 710
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 factors for every whole number. Always remember to include 1 and the number itself.
For example, in factors of 710, 1 and 710 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 710 consist of -1, -2, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 710/1.5 = 473.333, 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 710 are prime numbers.
For example, 2, 5, and 71 are the prime factors of 710, but it has other factors like 10, 142.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 710 as 2 × 5 × 71 and missing all the key factors.
Factors of 710 Examples
Problem 1
There are 10 friends and 710 marbles. How will they divide it equally?
They will get 71 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of friends.
710/10 = 71
Problem 2
A field is rectangular, the length of the field is 5 meters and the total area is 710 square meters. Find the width?
142 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
710 = 5 × width
To find the value of width, we need to shift 5 to the left side.
710/5 = width
Width = 142.
Problem 3
There are 2 large boxes and 710 apples. How many apples will be in each box?
Each box will have 355 apples.
Explanation
To find the apples in each box, divide the total apples by the number of boxes.
710/2 = 355
Problem 4
In a class, there are 710 students, and 71 groups. How many students are there in each group?
There are 10 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
710/71 = 10
Problem 5
710 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 142 books.
Explanation
Divide total books with shelves.
710/5 = 142
FAQs on Factors of 710
1.What are the factors of 710?
2.Mention the prime factors of 710.
3.Is 710 a multiple of 5?
4.Mention the factor pairs of 710?
5.What is the square of 710?
6.How can children in Qatar use numbers in everyday life to understand Factors of 710?
7.What are some fun ways kids in Qatar can practice Factors of 710 with numbers?
8.What role do numbers and Factors of 710 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 710 skills?
Important Glossaries for Factors of 710
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 710 are 1, 2, 5, 10, 71, 142, 355, and 710.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 71 are prime factors of 710.
- 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 710 are (1, 710), (2, 355), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 710 is 2 × 5 × 71.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, identifying (10, 71) as a factor pair of 710.
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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.
