124 LearnersLast updated on May 26th, 2025
Factors of -176
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 -176, how they are used in real life, and tips to learn them quickly.
What are the Factors of -176?
The numbers that divide -176 evenly are known as factors of -176.
A factor of -176 is a number that divides the number without remainder.
The factors of -176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
Negative factors of -176: -1, -2, -4, -8, -11, -16, -22, -44, -88,
-176. Prime factors of -176: 2 and 11.
Prime factorization of -176: 24 × 11.
The sum of factors of 176 (ignoring the negative sign): 1 + 2 + 4 + 8 + 11 + 16 + 22 + 44 + 88 + 176 = 372
How to Find Factors of -176?
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 176. Identifying the numbers which are multiplied to get the number 176 is the multiplication method.
Step 1: Multiply 176 by 1, 176 × 1 = 176.
Step 2: Check for other numbers that give 176 after multiplying 2 × 88 = 176 4 × 44 = 176 8 × 22 = 176 11 × 16 = 176
Therefore, the positive factor pairs of 176 are: (1, 176), (2, 88), (4, 44), (8, 22), (11, 16).
For every positive factor, there is a negative factor.
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 176 by 1, 176 ÷ 1 = 176.
Step 2: Continue dividing 176 by the numbers until the remainder becomes 0.
176 ÷ 1 = 176
176 ÷ 2 = 88
176 ÷ 4 = 44
176 ÷ 8 = 22
176 ÷ 11 = 16
Therefore, the factors of 176 are: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176.
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 176 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
The prime factors of 176 are 2 and 11.
The prime factorization of 176 is: 2^4 × 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, 176 is divided by 2 to get 88.
Step 2: Now divide 88 by 2 to get 44.
Step 3: Then divide 44 by 2 to get 22.
Step 4: Divide 22 by 2 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 176 is: 24 × 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 176: (1, 176), (2, 88), (4, 44), (8, 22), and (11, 16).
Negative factor pairs of 176: (-1, -176), (-2, -88), (-4, -44), (-8, -22), and (-11, -16).
Common Mistakes and How to Avoid Them in Factors of -176
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 176, 1 and 176 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 factors of -176 consist of -1, -2, -4, 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 176/1.5 = 117.333, 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 176 are prime numbers. For example, 2 and 11 are the prime factors of 176, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 176 as 2^4 × 11 and missing all the key factors.
Factors of -176 Examples
Problem 1
There are 176 apples and 8 baskets. How will you distribute them equally?
Each basket will have 22 apples.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of baskets.
176 ÷ 8 = 22
Problem 2
A room is rectangular, the width of the room is 16 meters and the total area is 176 square meters. Find the length?
11 meters.
Explanation
To find the length of the room, we use the formula
Area = length × width
176 = 16 × length
To find the value of length, we need to shift 16 to the left side.
176 ÷ 16 = length
Length = 11.
Problem 3
There are 44 students and 176 pencils. How many pencils will each student get?
Each student will get 4 pencils.
Explanation
To find the pencils each student gets, divide the total pencils by the number of students.
176 ÷ 44 = 4
Problem 4
In a club, there are 176 members, and 11 teams. How many members are there in each team?
There are 16 members in each team.
Explanation
Dividing the members by the total teams, we will get the number of members in each team.
176 ÷ 11 = 16
Problem 5
176 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 88 books.
Explanation
Divide total books by shelves.
176 ÷ 2 = 88
FAQs on Factors of -176
1.What are the factors of -176?
2.Mention the prime factors of -176.
3.Is -176 a multiple of 4?
4.Mention the factor pairs of -176?
5.What is the square of 176?
6.How can children in India use numbers in everyday life to understand Factors of -176?
7.What are some fun ways kids in India can practice Factors of -176 with numbers?
8.What role do numbers and Factors of -176 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -176 skills?
Important Glossaries for Factor of -176
- Factors: The numbers that divide a given number without leaving a remainder are called factors. For example, the factors of -176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
- Prime factors: The factors which are prime numbers. For example, 2 and 11 are prime factors of -176.
- 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 -176 are (1, 176), (2, 88), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of -176 is 2^4 × 11.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
