126 LearnersLast updated on May 26th, 2025
Factors of -105
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.
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
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
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.
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.
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.
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).
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
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 -105, 1 and -105 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -105 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because -105/1.5 = -70, 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 -105 are prime numbers.
For example, 3, 5, and 7 are the prime factors of -105, but it has other factors like 15, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -105 as -1 × 3 × 5 × 7 and missing all the key factors.
Factors of -105 Examples
Problem 1
A group of 5 friends has -105 points, how many points did each friend lose if divided equally?
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
Problem 2
A loss of -105 dollars is to be shared among 7 investors equally. How much loss does each investor bear?
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
Problem 3
A game has -105 penalty points to be distributed among 3 players. How many penalty points does each player get?
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
Problem 4
A team lost -105 goals over 15 matches. How many goals did they lose per match?
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
Problem 5
A company has a debt of -105 dollars spread over 21 months. What is the monthly debt?
The monthly debt is 5 dollars.
Explanation
Divide the total debt by the number of months to find the monthly debt.
-105/21 = -5
FAQs on Factors of -105
1.What are the factors of -105?
2.Mention the prime factors of -105.
3.Is -105 a multiple of 7?
4.Mention the factor pairs of -105?
5.What is the square of -105?
6.How can children in Indonesia use numbers in everyday life to understand Factors of -105?
7.What are some fun ways kids in Indonesia can practice Factors of -105 with numbers?
8.What role do numbers and Factors of -105 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of -105 skills?
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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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
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