Factors of 168
2026-02-28 11:19 Diff
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Last updated on December 11, 2025

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 168, how they are used in real life, and 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 = 360

How to Find Factors of 168?

Factors can be found using different methods. Mentioned below are some commonly used methods:

  1. Finding factors using multiplication
  2. Finding factors using division method
  3. 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). All these factor pairs result in 168. For every positive factor, there is a negative factor.

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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 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 them 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: 2³ × 3 × 7.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

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.

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Problem 1

There are 7 teams and 168 participants. How will they divide them equally?

Okay, lets begin

They will have 24 participants each.

Explanation

To divide the participants equally, we need to divide the total participants by the number of teams.

168/7 = 24

Well explained 👍

Problem 2

A room is rectangular, the width of the room is 14 meters and the total area is 168 square meters. Find the length?

Okay, lets begin

12 meters.

Explanation

To find the length of the room, we use the formula,

Area = length × width

168 = length × 14

To find the value of length, we need to shift 14 to the left side.

168/14 = length

Length = 12.

Well explained 👍

Problem 3

There are 24 boxes and 168 apples. How many apples will be in each box?

Okay, lets begin

Each box will have 7 apples.

Explanation

To find the apples in each box, divide the total apples by the boxes.

168/24 = 7

Well explained 👍

Problem 4

In a school, there are 168 students, and 6 buses. How many students are there in each bus?

Okay, lets begin

There are 28 students in each bus.

Explanation

Dividing the students by the total buses,

we will get the number of students in each bus.

168/6 = 28

Well explained 👍

Problem 5

168 books need to be arranged in 12 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 14 books.

Explanation

Divide total books by shelves.

168/12 = 14

Well explained 👍

FAQs on Factors of 168

1.What are the factors of 168?

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are the factors of 168.

2.Mention the prime factors of 168.

The prime factors of 168 are 2³ × 3 × 7.

3.Is 168 a multiple of 4?

4.Mention the factor pairs of 168?

(1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14) are the factor pairs of 168.

5.What is the square of 168?

Important Glossaries for Factor 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, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
  • 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.
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 168 is 2³ × 3 × 7.
  • Multiple: A multiple is a number that can be divided by another number without a remainder. For example, 168 is a multiple of 4.

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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.