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206 LearnersLast updated on December 16, 2025
Factors of -140
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 -140, how they are used in real life, and tips to learn them quickly.
What are the Factors of -140?
The numbers that divide -140 evenly are known as factors of -140.
A factor of -140 is a number that divides the number without a remainder.
The factors of -140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
Negative factors of -140: -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -70, and -140.
Prime factors of -140: 2, 5, and 7.
Prime factorization of -140: -1 × 2^2 × 5 × 7.
The sum of factors of 140 (ignoring the negative sign): 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 70 + 140 = 336
| Factor Type | Values |
| Positive Factors of -140 | (1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140.) |
| Negative Factors of -140 | (-1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -70, -140) |
| Prime Factors of -140 | (2, 5, 7) |
| Prime Factorization of -140 | -1 × 22 × 5 × 7 |
| Sum of factors of -140 | 336 |
How to Find Factors of -140?
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 140 (ignoring the negative sign initially). Identifying the numbers which are multiplied to get the number 140 is the multiplication method.
Step 1: Multiply 140 by 1, 140 × 1 = 140.
Step 2: Check for other numbers that give 140 after multiplying
2 × 70 = 140
4 × 35 = 140
5 × 28 = 140
7 × 20 = 140
10 × 14 = 140
Therefore, the positive factor pairs of 140 are: (1, 140), (2, 70), (4, 35), (5, 28), (7, 20), and (10, 14).
For every positive factor, there is a corresponding negative factor for -140.
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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 140 by 1, 140 ÷ 1 = 140.
Step 2: Continue dividing 140 by the numbers until the remainder becomes 0.
140 ÷ 1 = 140
140 ÷ 2 = 70
140 ÷ 4 = 35
140 ÷ 5 = 28
140 ÷ 7 = 20
140 ÷ 10 = 14
Therefore, the factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, and their negative counterparts for -140.
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 -140
Divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
140 ÷ 2 = 70
70 ÷ 2 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of -140 are 2, 5, and 7.
Prime Factorization of -140
Prime factorization of −140, first separate the negative sign from the number.
Step 1: Factor the absolute value
140 = 2 × 70
70 = 2 × 35
35 = 5 × 7
So,
140 = 2 × 2 × 5 × 7
= 22 × 5 × 7
Step 2: Include the negative sign
−140= −1 × 22 × 5 × 7
Factor Pairs of -140
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
| Factors | Positive Pair Factors |
| 1 × −140 = −140 | 1, −140 |
| 2 × −70 = −140 | 2, −70 |
| 4 × −35 = −140 | 4, −35 |
| 5 × −28 = −140 | 5, −28 |
| 7 × −20 = −140 | 7, −20 |
| 10 × −14 = −140 | 10, −14 |
Since the product of one positive number and one negative number is negative, −140 has positive–negative pair factors.
| Factors | Negative Pair Factors |
| −1 × 140 = −140 | −1, 140 |
| −2 × 70 = −140 | −2, 70 |
| −4 × 35 = −140 | −4, 35 |
| −5 × 28 = −140 | −5, 28 |
| −7 × 20 = −140 | −7, 20 |
| −10 × 14 = −140 | −10, 14 |
Common Mistakes and How to Avoid Them in Factors of -140
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 -140, 1 and 140 are also factors, along with their negative counterparts.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -140 consist of -1, -2, -4, etc.
Mistake 3
Including Fractions
Children might sometimes mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 140/1.5 = 93.333, 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 -140 are prime numbers.
For example, 2, 5, and 7 are the prime factors of -140, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking -140 as -1 × 2^2 × 5 × 7 and missing key factors.
Factors of -140 Examples
Problem 1
There are 7 teams and -140 points to distribute equally. How many points will each team get?
Each team will receive -20 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
-140/7 = -20
Problem 2
A swimming pool is 14 meters long, and the total area is -140 square meters. What is the width of the pool?
-10 meters.
Explanation
To find the width of the pool, we use the formula,
Area = length × width
-140 = 14 × width
To find the value of width, we need to shift 14 to the left side.
-140/14 = width Width = -10.
Problem 3
A Target store in Los Angeles (LA) discovers a system error while reconciling grocery bills and sales tax. The system shows a −140 USD adjustment that must be divided into equal whole-dollar corrections across departments. What are all the factors of −140 that represent possible equal splits?
−1, −2, −4, −5, −7, −10, −14, −20, −28, −35, −70, −140, 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Explanation
To find factors of −140, first factor the positive number 140.
Prime factorization:
140 = 2 × 2 × 5 × 7
Using these primes, all positive factors of 140 are generated.
Because the original number is negative, each positive factor also has a negative version.
Therefore, all integers ±1 through ±140 that divide evenly are factors of −140.
Problem 4
In a Boston middle-school science lab, students analyze inventory data used by CVS pharmacies. A simulation shows a −140 mg correction in medicine dosage due to overcounting. The dosage must be split into equal integer amounts. Which integers are factors of −140?
−1, −2, −4, −5, −7, −10, −14, −20, −28, −35, −70, −140, 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Explanation
A factor is a number that divides −140 exactly with no remainder.
Since −140 is negative, valid factors include both positive and negative integers.
All factors of 140 come from combinations of 2 × 2 × 5 × 7, and each has a corresponding negative factor.
Together, these form the complete factor list of −140.
Problem 5
An NBA team in Dallas reviews travel expenses after a road trip to Houston. A data error shows a −140 gallon fuel correction based on gas prices per gallon. The total loss must be divided evenly across fuel entries. What are all the factors of −140 that allow an exact split?
−1, −2, −4, −5, −7, −10, −14, −20, −28, −35, −70, −140, 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Explanation
Equal division requires numbers that divide −140 without leaving a remainder.
The absolute value 140 has multiple factor pairs formed from its prime factors.
Because the total correction is negative, both positive and negative divisors apply.
Thus, all ± factors of 140 are valid factors of −140.
FAQs on Factors of -140
1.What are the factors of -140?
2.Mention the prime factors of -140.
3.Is -140 a multiple of 7?
4.Mention the factor pairs of -140?
5.What is the absolute value of -140?
6.How many factors does −140 have?
7.What is the smallest factor of −140?
8.What is the largest factor of −140?
9.Which factors of −140 add up to 13?
10.How many even factors does −140 have?
11.What are the odd factors of −140?
12.What is the sum of all the factors of −140?
Important Glossaries for Factors of -140
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, and their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of -140.
- 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 -140 are (1, 140), (2, 70), etc., and their negative counterparts.
- Prime factorization: Breaking down a number into its prime factors. For -140, it is -1 × 22 × 5 × 7.
- Negative factors: The negative counterparts of the positive factors. For example, -1, -2, -4, etc., are negative factors of -140.
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.
