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218 LearnersLast updated on December 16, 2025
Factors of -126
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 -126, how they are used in real life, and tips to learn them quickly.
What are the Factors of -126?
The numbers that divide -126 evenly are known as factors of -126. A factor of -126 is a number that divides the number without a remainder.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
Negative factors of -126: -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, and -126.
Prime factors of -126: 2, 3, and 7.
Prime factorization of -126: -1 × 2 × 32 × 7.
The sum of factors of 126 (ignoring the negative factors): 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126 = 312
The factors of -126 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of -126 | (1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.) |
| Negative Factors of -126 | (-1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126) |
| Prime Factors of -126 | (2, 3, 7) |
| Prime Factorization of -126 | -1 × 2 × 32 × 7 |
| Sum of factors of -126 | 312 |
How to Find Factors of -126?
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 126. Identifying the numbers which are multiplied to get the number 126 is the multiplication method.
Step 1: Multiply 126 by 1, 126 × 1 = 126.
Step 2: Check for other numbers that give 126 after multiplying
- 2 × 63 = 126
- 3 × 42 = 126
- 6 × 21 = 126
- 7 × 18 = 126
- 9 × 14 = 126
Therefore, the positive factor pairs of 126 are: (1, 126), (2, 63), (3, 42), (6, 21), (7, 18), (9, 14). For every positive factor, there is a negative factor.
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Finding Factors Using Division Method
Dividing the given numbers with 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 126 by 1, 126 ÷ 1 = 126.
Step 2: Continue dividing 126 by the numbers until the remainder becomes 0.
- 126 ÷ 1 = 126
- 126 ÷ 2 = 63
- 126 ÷ 3 = 42
- 126 ÷ 6 = 21
- 126 ÷ 7 = 18
- 126 ÷ 9 = 14
Therefore, the factors of 126 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
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 126
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
- 126 ÷ 2 = 63
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
- 7 ÷ 7 = 1
The prime factors of -126 are 2, 3, and 7.
Prime Factorization of -126
Prime Factorization breaks down the prime factors of -126.
Step 1: Firstly, 126 is divided by 2 to get 63.
Step 2: Now divide 63 by 3 to get 21.
Step 3: Then divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -126 is: -1 × 2 × 32 × 7.
Factor Pairs of -126
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 126:
| Factors | Positive Pair Factors |
| 1 × −126 = −126 | 1, −126 |
| 2 × −63 = −126 | 2, −63 |
| 3 × −42 = −126 | 3, −42 |
| 6 × −21 = −126 | 6, −21 |
| 7 × −18 = −126 | 7, −18 |
| 9 × −14 = −126 | 9, −14 |
Negative factor pairs of -126:
| Factors | Negative Pair Factors |
| −1 × 126 = −126 | −1, 126 |
| −2 × 63 = −126 | −2, 63 |
| −3 × 42 = −126 | −3, 42 |
| −6 × 21 = −126 | −6, 21 |
| −7 × 18 = −126 | −7, 18 |
| −9 × 14 = −126 | −9, 14 |
Common Mistakes and How to Avoid Them in Factors of -126
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 word. Always remember to include 1 and the number itself.
For example, in factors of -126, 1 and 126 are also factors.
Mistake 2
Missing Negative Factors
We have often mentioned only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -126 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 126/1.5 = 84, 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 -126 are prime numbers.
For example, 2, 3, and 7 are the prime factors of -126, but it has other factors like 9, 42.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -126 as -1 × 2 × 32 × 7 and missing all the key factors.
Factors of -126 Examples
Problem 1
There are 9 friends and 126 candies. How will they divide it equally?
They will get 14 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
126/9 = 14
Problem 2
A field is rectangular, the length of the field is 18 meters, and the total area is 126 square meters. Find the width?
7 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width
126 = 18 × width
To find the value of width, we need to shift 18 to the left side.
126/18 = width
Width = 7.
Problem 3
A Walmart store in New York City finds a bookkeeping error after applying sales tax refunds. The accounting system shows a โ126 USD correction that must be divided into equal whole-dollar adjustments across departments. What are all the factors of โ126 that represent possible equal splits?
−1, −2, −3, −6, −7, −9, −14, −18, −21, −42, −63, −126, 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Explanation
First find the factors of 126.
Prime factorization:
126 = 2 × 3 × 3 × 7
Using these primes, all positive divisors of 126 are generated.
Since the original number is negative, every positive factor also has a negative counterpart.
Thus, all ± divisors of 126 are factors of −126.
Problem 4
In a Boston middle-school science class, students model inventory data from a CVS pharmacy. A simulated error shows a โ126 mg net change in medicine dosage that must be split into equal integer dosage units. Which integers are factors of โ126?
−1, −2, −3, −6, −7, −9, −14, −18, −21, −42, −63, −126, 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Explanation
A factor divides −126 evenly with no remainder.
The absolute value 126 has factors formed from 2 × 3² × 7.
Because the total change is negative, both positive and negative integers qualify as factors.
Therefore, all ± factors of 126 are valid.
Problem 5
An NFL team in Dallas reviews travel expenses after a road game in Houston. Due to a gas-price miscalculation (priced per gallon), the fuel log shows a โ126 gallon correction. The loss must be split evenly across fuel records. What are all the factors of โ126 that allow an exact split?
−1, −2, −3, −6, −7, −9, −14, −18, −21, −42, −63, −126, 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Explanation
Equal division requires integers that divide −126 without leaving a remainder.
The number 126 has multiple factor pairs based on its prime factors.
Since the correction is negative, each positive divisor also has a negative version.
Together, these form the complete factor set of −126.
FAQs on Factors of -126
1.What are the factors of -126?
2.Mention the prime factors of -126.
3.Is 126 a multiple of 9?
4.Mention the factor pairs of -126?
5.What is the square of -126?
6.How many factors does โ126 have?
7.What is the smallest factor of โ126?
8.What is the largest factor of โ126?
9.Which factors of โ126 add up to 13?
10.How many even factors does โ126 have?โ126 has 12 even factors.
11.What are the odd factors of โ126?
12.What is the sum of all the factors of โ126?
Important Glossaries for Factor of -126
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of -126.
- 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 126 are (1, 126), (2, 63), etc.
- Negative factors: These are the negative counterparts of the positive factors. For example, -1, -2, -3, -6, -7, etc., are negative factors of -126.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, -126 = -1 × 2 × 32 × 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.
