121 LearnersLast updated on May 26th, 2025
Factors of -168
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of -168, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -168?
The numbers that divide -168 evenly are known as factors of -168.
A factor of -168 is a number that divides the number without remainder.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
Negative factors of -168: -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84, and -168.
Prime factors of 168: 2, 3, and 7.
Prime factorization of 168: 23 × 3 × 7.
The sum of factors of 168: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 21 + 24 + 28 + 42 + 56 + 84 + 168 = 504
How to Find Factors of -168?
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 168. Identifying the numbers which are multiplied to get the number 168 is the multiplication method.
Step 1: Multiply 168 by 1, 168 × 1 = 168.
Step 2: Check for other numbers that give 168 after multiplying
2 × 84 = 168
3 × 56 = 168
4 × 42 = 168
6 × 28 = 168
7 × 24 = 168
8 × 21 = 168
12 × 14 = 168
Therefore, the positive factor pairs of 168 are: (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14).
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 the simple division method
Step 1: Divide 168 by 1, 168 ÷ 1 = 168.
Step 2: Continue dividing 168 by the numbers until the remainder becomes 0.
168 ÷ 1 = 168
168 ÷ 2 = 84
168 ÷ 3 = 56
168 ÷ 4 = 42
168 ÷ 6 = 28
168 ÷ 7 = 24
168 ÷ 8 = 21
168 ÷ 12 = 14
Therefore, the factors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
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 168 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 168 are 2, 3, and 7.
The prime factorization of 168 is: 2^3 × 3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 168 is divided by 2 to get 84.
Step 2: Now divide 84 by 2 to get 42.
Step 3: Then divide 42 by 2 to get 21.
Step 4: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 168 is: 23 × 3 × 7.
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 168: (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14).
Negative factor pairs of -168: (-1, -168), (-2, -84), (-3, -56), (-4, -42), (-6, -28), (-7, -24), (-8, -21), (-12, -14).
Common Mistakes and How to Avoid Them in Factors of -168
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 -168, 1 and -168 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 -168 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 168/1.5 ≠ 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 -168 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 168, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 168 as 2^3 × 3 × 7 and missing all the key factors.
Factors of -168 Examples
Problem 1
There are 14 teams and -168 points. How will the points be distributed equally among the teams?
Each team will receive -12 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
-168/14 = -12
Problem 2
An event had a total of -168 participants divided into 24 groups. How many participants were in each group?
Each group had -7 participants.
Explanation
To find the participants in each group, divide the total participants by the number of groups.
-168/24 = -7
Problem 3
There are -168 apples, and they need to be packed into 6 boxes. How many apples will go into each box?
Each box will contain -28 apples.
Explanation
To find the apples in each box, divide the total apples by the number of boxes.
-168/6 = -28
Problem 4
A company has -168 defective products to be equally divided among 12 inspectors. How many products will each inspector review?
Each inspector will review -14 products.
Explanation
Dividing the total defective products by the number of inspectors, we will get the number of products each inspector will review.
-168/12 = -14
Problem 5
A piece of fabric measuring -168 cm is cut into pieces of 14 cm each. How many pieces will be obtained?
12 pieces will be obtained.
Explanation
Divide the total length by the length of each piece.
-168/14 = -12
FAQs on Factors of -168
1.What are the factors of -168?
2.Mention the prime factors of -168.
3.Is -168 a multiple of 8?
4.Mention the factor pairs of -168?
5.What is the cube of -168?
Important Glossaries for Factors of -168
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -168 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 168.
- 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 -168 are (1, 168), (2, 84), etc.
- Negative factors: Negative numbers that divide the given number without leaving a remainder. For example, the negative factors of -168 are -1, -2, -3, etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 168 is 2^3 × 3 × 7.
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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.
