122 LearnersLast updated on May 26th, 2025
Factors of -154
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 -154, how they are used in real life, and tips to learn them quickly.
What are the Factors of -154?
The numbers that divide -154 evenly are known as factors of -154.
A factor of -154 is a number that divides the number without remainder.
The factors of -154 are 1, 2, 7, 11, 14, 22, 77, and 154.
Negative factors of -154: -1, -2, -7, -11, -14, -22, -77, and -154.
Prime factors of -154: 2, 7, and 11.
Prime factorization of -154: -1 × 2 × 7 × 11.
The sum of the absolute values of factors of -154: 1 + 2 + 7 + 11 + 14 + 22 + 77 + 154 = 288.
How to Find Factors of -154?
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 -154. Identifying the numbers which are multiplied to get the number -154 is the multiplication method.
Step 1: Multiply -154 by -1, -154 × -1 = 154.
Step 2: Check for other numbers that give 154 after multiplying
-2 × -77 = 154
-7 × -22 = 154
-11 × -14 = 154
Therefore, the positive factor pairs of 154 are: (1, 154), (2, 77), (7, 22), (11, 14).
For every positive factor, there is a negative factor.
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 -154 by -1, -154 ÷ -1 = 154.
Step 2: Continue dividing -154 by the numbers until the remainder becomes 0.
-154 ÷ -1 = 154
-154 ÷ -2 = 77
-154 ÷ -7 = 22
-154 ÷ -11 = 14
Therefore, the factors of -154 are: 1, 2, 7, 11, 14, 22, 77, 154.
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 154 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
154 ÷ 2 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 154 are 2, 7, and 11.
The prime factorization of -154 is: -1 × 2 × 7 × 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, 154 is divided by 2 to get 77.
Step 2: Now divide 77 by 7 to get 11.
Step 3: Divide 11 by 11 to get 1. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of -154 is: -1 × 2 × 7 × 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 -154: (1, 154), (2, 77), (7, 22), (11, 14).
Negative factor pairs of -154: (-1, -154), (-2, -77), (-7, -22), (-11, -14).
Common Mistakes and How to Avoid Them in Factors of -154
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 number. Always remember to include 1 and the number itself.
For example, in factors of -154, 1 and 154 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the negative factors of -154 consist of -1, -2, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -154/1.5 = -102.666..., 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 -154 are prime numbers.
For example, 2, 7, and 11 are some of the prime factors of -154, but it has other factors like 14, 22.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -154 as -1 × 2 × 7 × 11 and missing all the key factors.
Factors of -154 Examples
Problem 1
There are 7 groups of people and -154 apples. If each group takes an equal share of apples, how many apples does each group get?
Each group gets -22 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of groups.
-154/7 = -22
Problem 2
A machine produces -154 widgets in 11 hours. How many widgets does it produce per hour?
-14 widgets per hour.
Explanation
To find the production rate per hour, use the formula:
Total widgets = widgets per hour × total hours
-154 = widgets per hour × 11
Widgets per hour = -154/11 = -14
Problem 3
There are -154 candies and 2 boxes. How many candies will be in each box?
Each box will have -77 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
-154/2 = -77
Problem 4
A company has -154 tasks to complete and plans to finish them in 14 days. How many tasks should they complete each day?
-11 tasks each day.
Explanation
Dividing the tasks by the number of days, we will get the number of tasks to complete each day.
-154/14 = -11
Problem 5
An artist has -154 units of a special paint and uses it at a rate of 11 units per project. How many projects can the artist complete?
The artist can complete 14 projects.
Explanation
Divide the total paint units by the units used per project.
-154/11 = -14
FAQs on Factors of -154
1.What are the factors of -154?
2.Mention the prime factors of -154.
3.Is -154 a multiple of 11?
4.Mention the factor pairs of -154?
5.What is the absolute value sum of factors of -154?
6.How can children in India use numbers in everyday life to understand Factors of -154?
7.What are some fun ways kids in India can practice Factors of -154 with numbers?
8.What role do numbers and Factors of -154 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -154 skills?
Important Glossaries for Factors of -154
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -154 are 1, 2, 7, 11, 14, 22, 77, and 154.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 11 are prime factors of -154.
- 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 -154 are (1, 154), (2, 77), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -7, etc., are negative factors of -154.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of -154 is -1 × 2 × 7 × 11.
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About BrightChamps in India
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.
