120 LearnersLast updated on May 26th, 2025
Factors of -210
Factors are the numbers that divide any given number evenly without a 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 -210, how they are used in real life, and tips to learn them quickly.
What are the Factors of -210?
The numbers that divide -210 evenly are known as factors of -210.
A factor of -210 is a number that divides the number without a remainder.
The factors of -210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
Negative factors of -210: -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105, and -210.
Prime factors of -210: 2, 3, 5, and 7.
Prime factorization of -210: 2 × 3 × 5 × 7.
The sum of factors of 210 (ignoring the sign): 1 + 2 + 3 + 5 + 6 + 7 + 10 + 14 + 15 + 21 + 30 + 35 + 42 + 70 + 105 + 210 = 768
How to Find Factors of -210?
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 -210. Identifying the numbers which are multiplied to get the number -210 is the multiplication method.
Step 1: Multiply -210 by -1, -210 × -1 = 210.
Step 2: Check for other numbers that give -210 after multiplying:
(-2) × 105 = -210
(-3) × 70 = -210
(-5) × 42 = -210
(-6) × 35 = -210
(-7) × 30 = -210
(-10) × 21 = -210
(-14) × 15 = -210
Therefore, the positive factor pairs of -210 are: (1, -210), (2, -105), (3, -70), (5, -42), (6, -35), (7, -30), (10, -21), (14, -15).
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 -210 by -1, -210 ÷ -1 = 210.
Step 2: Continue dividing -210 by the numbers until the remainder becomes 0.
-210 ÷ -1 = 210
-210 ÷ -2 = 105
-210 ÷ -3 = 70
-210 ÷ -5 = 42
-210 ÷ -6 = 35
-210 ÷ -7 = 30
-210 ÷ -10 = 21
-210 ÷ -14 = 15
Therefore, the factors of -210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 -210 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of -210 are 2, 3, 5, and 7.
The prime factorization of -210 is: 2 × 3 × 5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 210 is divided by 2 to get 105.
Step 2: Now divide 105 by 3 to get 35.
Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -210 is: 2 × 3 × 5 × 7. 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 -210: (1, -210), (2, -105), (3, -70), (5, -42), (6, -35), (7, -30), (10, -21), (14, -15).
Negative factor pairs of -210: (-1, 210), (-2, 105), (-3, 70), (-5, 42), (-6, 35), (-7, 30), (-10, 21), (-14, 15).
Common Mistakes and How to Avoid Them in Factors of -210
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 number. Always remember to include 1 and the number itself.
For example, in factors of -210, 1 and -210 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of -210 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because -210/1.5 = -140, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes. For example, thinking all the factors of -210 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of -210, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -210 as 2 × 3 × 5 × 7 and missing all the key factors.
Factors of -210 Examples
Problem 1
There are 7 trucks and -210 kilograms of load. How will they divide it equally?
Each truck will carry -30 kilograms.
Explanation
To divide the load equally, we need to divide the total load by the number of trucks.
-210/7 = -30
Problem 2
A garden is rectangular, the width of the garden is 15 meters, and the total area is -210 square meters. Find the length.
-14 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
-210 = length × 15
To find the value of length, we need to solve for length.
-210/15 = length
Length = -14.
Problem 3
There are 30 boxes and -210 marbles. How many marbles will be in each box?
Each box will have -7 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
-210/30 = -7
Problem 4
In a class, there are -210 students and 5 groups. How many students are there in each group?
Each group has -42 students.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
-210/5 = -42
Problem 5
-210 books need to be arranged in 14 shelves. How many books will go on each shelf?
Each of the shelves will have -15 books.
Explanation
Divide the total books by shelves.
-210/14 = -15
FAQs on Factors of -210
1.What are the factors of -210?
2.Mention the prime factors of -210.
3.Is -210 a multiple of 6?
4.Mention the factor pairs of -210?
5.What is the square of 210?
6.How can children in Qatar use numbers in everyday life to understand Factors of -210?
7.What are some fun ways kids in Qatar can practice Factors of -210 with numbers?
8.What role do numbers and Factors of -210 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -210 skills?
Important Glossaries for Factors of -210
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of -210.
- 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 -210 are (1, -210), (2, -105), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, -5, etc., are negative factors of -210.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of -210 is 2 × 3 × 5 × 7.
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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.
