Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 14 teams and -168 points. How will the points be distributed equally among the teams?
Each team will receive -12 points.
To distribute the points equally, we need to divide the total points by the number of teams.
-168/14 = -12
An event had a total of -168 participants divided into 24 groups. How many participants were in each group?
Each group had -7 participants.
To find the participants in each group, divide the total participants by the number of groups.
-168/24 = -7
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.
To find the apples in each box, divide the total apples by the number of boxes.
-168/6 = -28
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.
Dividing the total defective products by the number of inspectors, we will get the number of products each inspector will review.
-168/12 = -14
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.
Divide the total length by the length of each piece.
-168/14 = -12
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.
: She loves to read number jokes and games.