122 LearnersLast updated on May 26th, 2025
Factors of -110
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 -110, how they are used in real life, and tips to learn them quickly.
What are the Factors of -110?
The numbers that divide -110 evenly are known as factors of -110.
A factor of -110 is a number that divides the number without remainder.
The factors of -110 are 1, 2, 5, 10, 11, 22, 55, and 110.
Negative factors of -110: -1, -2, -5, -10, -11, -22, -55, and -110.
Prime factors of -110: 2, 5, and 11.
Prime factorization of -110: -1 × 2 × 5 × 11.
The sum of factors of 110 (ignoring the negative sign): 1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 = 216
How to Find Factors of -110?
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 multiply to give -110. Identifying the numbers multiplied to get the number -110 is the multiplication method.
Step 1: Multiply -110 by 1, -110 × 1 = -110.
Step 2: Check for other numbers that give -110 after multiplying:
2 × -55 = -110
5 × -22 = -110
10 × -11 = -110
Therefore, the positive factor pairs of -110 are: (1, -110), (2, -55), (5, -22), (10, -11).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following this simple division method:
Step 1: Divide -110 by 1, -110 ÷ 1 = -110.
Step 2: Continue dividing -110 by the numbers until the remainder becomes 0.
-110 ÷ 1 = -110
-110 ÷ 2 = -55
-110 ÷ 5 = -22
-110 ÷ 10 = -11
Therefore, the factors of -110 are: 1, 2, 5, 10, 11, 22, 55, 110.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 -110 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
-110 ÷ 2 = -55
-55 ÷ 5 = -11
-11 ÷ 11 = -1
The prime factors of -110 are 2, 5, and 11.
The prime factorization of -110 is: -1 × 2 × 5 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, -110 is divided by 2 to get -55.
Step 2: Now divide -55 by 5 to get -11.
Step 3: Divide -11 by 11 to get -1. The prime factorization of -110 is: -1 × 2 × 5 × 11.
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 -110: (1, -110), (2, -55), (5, -22), and (10, -11).
Negative factor pairs of -110: (-1, 110), (-2, 55), (-5, 22), and (-10, 11).
Common Mistakes and How to Avoid Them in Factors of -110
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 -110, 1 and -110 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 -110 include -1, -2, -5, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor, because -110/1.5 = -73.333, and it is not a whole number.
Mistake 4
Confusing Factors with Prime Numbers
Remember that factors can be any whole number, not just primes.
For example, thinking all the factors of -110 are prime numbers.
For example, 2, 5, and 11 are the prime factors of -110, but it has other factors like 10, 22.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking -110 as -1 × 2 × 5 × 11 and missing all the key factors.
Factors of -110 Examples
Problem 1
There are 11 boxes and -110 items. How many items will go in each box if distributed equally?
Each box will have -10 items.
Explanation
To distribute the items equally, divide the total items by the number of boxes.
-110/11 = -10
Problem 2
A rope is -110 meters long and needs to be cut into 10 equal pieces. What will be the length of each piece?
Each piece will be -11 meters long.
Explanation
To find the length of each piece, divide the total length by the number of pieces.
-110/10 = -11
Problem 3
There are 5 bags and -110 apples. How many apples will go in each bag?
Each bag will have -22 apples.
Explanation
To find the apples in each bag, divide the total apples by the number of bags.
-110/5 = -22
Problem 4
A bridge is -110 meters long and divided into 2 equal sections. What is the length of each section?
Each section is -55 meters long.
Explanation
Divide the total length by the number of sections to find the length of each section.
-110/2 = -55
Problem 5
-110 books need to be arranged in 11 stacks. How many books will go in each stack?
Each stack will have -10 books.
Explanation
Divide the total number of books by stacks.
-110/11 = -10
FAQs on Factors of -110
1.What are the factors of -110?
2.Mention the prime factors of -110.
3.Is -110 a multiple of 5?
4.Mention the factor pairs of -110.
5.What is the absolute value of -110?
Important Glossaries for Factor of -110
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -110 are 1, 2, 5, 10, 11, 22, 55, and 110.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 11 are prime factors of -110.
- 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 -110 are (1, -110), (2, -55), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -5 are negative factors of -110.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find factors of -110.
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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.
