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Last updated on May 26th, 2025

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Factors of -105

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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 -105, how they are used in real life, and the tips to learn them quickly.

Factors of -105 for Indonesian Students
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What are the Factors of -105?

The numbers that divide -105 evenly are known as factors of -105.

 

A factor of -105 is a number that divides the number without remainder.

 

The factors of -105 are 1, 3, 5, 7, 15, 21, 35, and 105.

 

Negative factors of -105: -1, -3, -5, -7, -15, -21, -35, and -105.

 

Prime factors of -105: 3, 5, and 7.

 

Prime factorization of -105: -1 × 3 × 5 × 7.

 

The sum of factors of 105: 1 + 3 + 5 + 7 + 15 + 21 + 35 + 105 = 192

factors of -105

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How to Find Factors of -105?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -105. Identifying the numbers which are multiplied to get the number -105 is the multiplication method.

 

Step 1: Multiply -105 by 1, -105 × 1 = -105.

 

Step 2: Check for other numbers that give -105 after multiplying

3 × -35 = -105

5 × -21 = -105

7 × -15 = -105

 

Therefore, the positive factor pairs of -105 are: (1, -105), (3, -35), (5, -21), (7, -15).

 

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given number 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 -105 by 1, -105 ÷ 1 = -105.

 

Step 2: Continue dividing -105 by the numbers until the remainder becomes 0.

 

-105 ÷ 1 = -105

-105 ÷ 3 = -35

-105 ÷ 5 = -21

-105 ÷ 7 = -15

 

Therefore, the factors of -105 are: 1, 3, 5, 7, 15, 21, 35, 105.

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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 -105 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

-105 ÷ -1 = 105

105 ÷ 3 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

 

The prime factors of -105 are 3, 5, and 7.

 

The prime factorization of -105 is: -1 × 3 × 5 × 7.

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Factor Tree

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

 

Step 1: Firstly, -105 is divided by -1 to get 105.

 

Step 2: Now divide 105 by 3 to get 35.

 

Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -105 is: -1 × 3 × 5 × 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 -105: (1, -105), (3, -35), (5, -21), and (7, -15).

 

Negative factor pairs of -105: (-1, 105), (-3, 35), (-5, 21), and (-7, 15).

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Common Mistakes and How to Avoid Them in Factors of -105

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

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Forgetting the number itself and 1 is a factor

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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 -105, 1 and -105 are also factors.

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Factors of -105 Examples

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Problem 1

A group of 5 friends has -105 points, how many points did each friend lose if divided equally?

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Each friend lost 21 points.

Explanation

To divide the points equally, we need to divide the total points by the number of friends.

 

-105/5 = -21

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Problem 2

A loss of -105 dollars is to be shared among 7 investors equally. How much loss does each investor bear?

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Each investor bears a loss of 15 dollars.

Explanation

To find the loss per investor, we divide the total loss by the number of investors.

 

-105/7 = -15

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Problem 3

A game has -105 penalty points to be distributed among 3 players. How many penalty points does each player get?

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Each player gets 35 penalty points.

Explanation

To find the penalty points per player, divide the total penalty points by the number of players.

 

-105/3 = -35

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Problem 4

A team lost -105 goals over 15 matches. How many goals did they lose per match?

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They lost 7 goals per match.

Explanation

Dividing the total goals lost by the number of matches gives us the goals lost per match.

 

-105/15 = -7

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Problem 5

A company has a debt of -105 dollars spread over 21 months. What is the monthly debt?

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The monthly debt is 5 dollars.

Explanation

Divide the total debt by the number of months to find the monthly debt.

 

-105/21 = -5

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FAQs on Factors of -105

1.What are the factors of -105?

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2.Mention the prime factors of -105.

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3.Is -105 a multiple of 7?

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4.Mention the factor pairs of -105?

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5.What is the square of -105?

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6.How can children in Indonesia use numbers in everyday life to understand Factors of -105?

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7.What are some fun ways kids in Indonesia can practice Factors of -105 with numbers?

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8.What role do numbers and Factors of -105 play in helping children in Indonesia develop problem-solving skills?

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9.How can families in Indonesia create number-rich environments to improve Factors of -105 skills?

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Professor Greenline from BrightChamps

Important Glossaries for Factors of -105

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -105 are 1, 3, 5, 7, 15, 21, 35, and 105.
     
  • Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of -105.
     
  • Negative factors: Factors that are negative numbers. For example, -1, -3, -5, etc., are negative factors of -105.
     
  • 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 -105 are (1, -105), (3, -35), etc.
     
  • Prime factorization: The process of breaking down a number into its prime factors. For example, prime factorization of -105 is -1 × 3 × 5 × 7.
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About BrightChamps in Indonesia

At BrightChamps, numbers are more than just digits—they’re gateways to many opportunities! We strive to help children across Indonesia master vital math skills, focusing today on Factors of -105 with special attention to factors—in a fun, clear, and engaging way. Whether your child is calculating the speed of a ride at Dunia Fantasi, tracking scores at badminton matches, or managing their allowance for gadgets, solid number skills give them confidence in daily life. Our hands-on lessons make learning both fun and straightforward. Since kids in Indonesia learn in varied ways, we adapt our teaching to each child’s needs. From Jakarta’s busy streets to Bali’s beautiful beaches, BrightChamps brings math to life throughout Indonesia. Let’s make factors an enjoyable part of every child’s math adventure!
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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.

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Fun Fact

: She loves to read number jokes and games.

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