121 LearnersLast updated on May 26th, 2025
Factors of -121
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 -121, how they are used in real life, and tips to learn them quickly.
What are the Factors of -121?
The numbers that divide -121 evenly are known as factors of -121.
A factor of -121 is a number that divides the number without remainder.
Positive factors of 121: 1, 11, 121.
Negative factors of -121: -1, -11, and -121.
Prime factors of 121: 11.
Prime factorization of 121: 11 × 11.
The sum of factors of -121 (considering only positive factors): 1 + 11 + 121 = 133
How to Find Factors of -121?
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 are multiplied to give -121. Identifying the numbers which are multiplied to get the number -121 is the multiplication method.
Step 1: Multiply -121 by 1, -121 × 1 = -121.
Step 2: Check for other numbers that give -121 after multiplying 11 × -11 = -121 Therefore, the positive factor pairs of -121 are: (1, -121) and (11, -11).
All these factor pairs result in -121.
For every positive factor, there is a corresponding negative factor.
Finding Factors Using Division Method
Dividing the given number 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 the simple division method
Step 1: Divide -121 by 1, -121 ÷ 1 = -121.
Step 2: Continue dividing -121 by the numbers until the remainder becomes 0.
-121 ÷ 1 = -121
-121 ÷ 11 = -11
Therefore, the factors of -121 are: 1, -1, 11, -11, 121, -121.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 121 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factor of 121 is 11.
The prime factorization of 121 is: 11 × 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, 121 is divided by 11 to get 11.
Step 2: Now divide 11 by 11 to get 1. The prime factorization of 121 is: 11 × 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 -121: (1, -121) and (11, -11).
Negative factor pairs of -121: (-1, 121) and (-11, 11).
Common Mistakes and How to Avoid Them in Factors of -121
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 as 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 -121, 1 and -121 are also factors.
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 -121 consist of -1, -11, 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 -121/1.5 = -80.6667, 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 -121 are prime numbers.
For example, 11 is a prime factor of 121, but it has other factors like 1, 121.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 121 as 11 × 11 and missing key factors.
Factors of -121 Examples
Problem 1
There are 11 friends and -121 apples. How will they divide it equally?
They will get -11 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of friends.
-121/11 = -11
Problem 2
A field is rectangular, the length of the field is 11 meters and the total area is -121 square meters. Find the width?
-11 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width -121 = 11 × width
To find the value of width, we need to shift 11 to the left side.
-121/11 = width
Width = -11.
Problem 3
There are 121 bags and -121 marbles. How many marbles will be in each bag?
Each bag will have -1 marble.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
-121/121 = -1
Problem 4
In a class, there are -121 students, and 11 groups. How many students are there in each group?
There are -11 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
-121/11 = -11
Problem 5
-121 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has -11 books.
Explanation
Divide total books by shelves.
-121/11 = -11
FAQs on Factors of -121
1.What are the factors of -121?
2.Mention the prime factors of -121.
3.Is -121 a multiple of 11?
4.Mention the factor pairs of -121?
5.What is the square of 11?
Important Glossaries for Factors of -121
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -121 are 1, -1, 11, -11, 121, -121.
- Prime factors: The factors which are prime numbers. For example, 11 is a prime factor of 121.
- 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 -121 are (1, -121) and (11, -11).
- Prime factorization: The process of determining the prime numbers that multiply together to give a particular number. For example, the prime factorization of 121 is 11 × 11.
- Negative factors: Factors that are negative numbers, such as -1 and -11, are negative factors of -121.
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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.
