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230 LearnersLast updated on December 16, 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
The factors of -210 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of -210 | (1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210) |
| Negative Factors of -210 | (-1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105, -210) |
| Prime Factors of -210 | (2, 3, 5, 7) |
| Prime Factorization of -210 | 2 × 3 × 5 × 7 |
| Sum of factors of -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.
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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
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime Factors of -210
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
Divide 210 by 2,
- 210 ÷ 2 = 105
- 105 ÷ 3 = 35
- 35 ÷ 5 = 7
- 7 ÷ 7 = 1
The prime factors of -210 are 2, 3, 5, and 7.
Prime Factorization of -210
To find the prime factorization of −210, start by separating the negative sign from the number.
Step 1: Factor the absolute value
105 = 3 × 35
35 = 5 × 7
So,
210 = 2 × 3 × 5 × 7
Step 2: Include the negative sign
−210 = −1 × 2 × 3 × 5 × 7
Factor Pairs of -210
Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive Pair Factors of -210:
| Factors | Pair Factors |
| 1 × −210 = −210 | 1, −210 |
| 2 × −105 = −210 | 2, −105 |
| 3 × −70 = −210 | 3, −70 |
| 5 × −42 = −210 | 5, −42 |
| 6 × −35 = −210 | 6, −35 |
| 7 × −30 = −210 | 7, −30 |
| 10 × −21 = −210 | 10, −21 |
| 14 × −15 = −210 | 14, −15 |
Since the product of one positive number and one negative number is negative, -210 has positive - negative pair factors.
Negative Pair Factors of -210:
| Factors | Pair Factors |
| −1 × 210 = −210 | −1, 210 |
| −2 × 105 = −210 | −2, 105 |
| −3 × 70 = −210 | −3, 70 |
| −5 × 42 = −210 | −5, 42 |
| −6 × 35 = −210 | −6, 35 |
| −7 × 30 = −210 | −7, 30 |
| −10 × 21 = −210 | −10, 21 |
| −14 × 15 = −210 | −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
A Walmart store in Chicago finds a tax calculation error after closing accounts. The system shows a โ210 USD adjustment that must be split into equal whole-dollar corrections for internal records. What are all the factors of โ210 that represent possible equal splits?
−1, −2, −3, −5, −6, −7, −10, −14, −15, −21, −30, −35, −42, −70, −105, −210, 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Explanation
To find factors of −210, first find the factors of 210.
Prime factorization:
210 = 2 × 3 × 5 × 7
All positive factors are formed using these primes.
Since the original number is negative, every positive factor also has a negative counterpart.
Therefore, all integers ±1 through ±210 that divide evenly are factors of −210.
Problem 4
During a school science lab in Boston, students model medicine inventory tracking used by Walgreens. A simulated data error shows a โ210 mg change in total dosage due to overcounting. The correction must be split into equal integer dosage units. Which integers are factors of โ210?
−1, −2, −3, −5, −6, −7, −10, −14, −15, −21, −30, −35, −42, −70, −105, −210, 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Explanation
A factor is a number that divides −210 exactly with no remainder.
Since −210 is negative, valid factors include both positive and negative integers.
Using the prime factors of 210 (2, 3, 5, 7), all possible products give the full factor list.
Each positive factor also has a negative version, forming the complete set.
Problem 5
After an NFL game in Dallas, a team bus log shows a fuel accounting correction of โ210 gallons due to a data mismatch in gas prices (measured per gallon). The loss must be divided evenly across multiple fuel entries. What are all the factors of โ210 that allow an exact split?
−1, −2, −3, −5, −6, −7, −10, −14, −15, −21, −30, −35, −42, −70, −105, −210, 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Explanation
Equal splits require numbers that divide −210 evenly.
The absolute value 210 has multiple factor pairs formed from 2 × 3 × 5 × 7.
Because the total is negative, both positive and negative integers qualify.
Thus, all ± factors of 210 are factors of −210.
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 many factors does โ210 have?
7.What is the smallest factor of โ210?
8.What is the largest factor of โ210?
9.Which factors of โ210 add up to 13?
10.How many even factors does โ210 have?
11.What are the odd factors of โ210?
12.What is the sum of all the factors of โ210?
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.
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.
