Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 -10, how they are used in real life, and tips to learn them quickly.
The numbers that divide -10 evenly are known as factors of -10.
A factor of -10 is a number that divides the number without a remainder.
The factors of -10 include both positive and negative numbers: 1, -1, 2, -2, 5, -5, 10, and -10.
Prime factors of -10: 2 and 5.
Prime factorization of -10: -1 × 2 × 5.
The sum of the positive factors of 10: 1 + 2 + 5 + 10 = 18
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify pairs of numbers that multiply to give -10. Identifying the numbers which are multiplied to get the number -10 is the multiplication method.
Step 1: Multiply -10 by 1, -10 × 1 = -10.
Step 2: Check for other numbers that give -10 after multiplying
2 × -5 = -10
-2 × 5 = -10
Therefore, the positive and negative factor pairs of -10 are: (1, -10), (-1, 10), (2, -5), and (-2, 5). All these factor pairs result in -10.
Dividing the given number by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide -10 by 1, -10 ÷ 1 = -10.
Step 2: Continue dividing -10 by the numbers until the remainder becomes 0.
(-10 ÷ 1 = -10
-10 ÷ -1 = 10
-10 ÷ 2 = -5
-10 ÷ -2 = 5
Therefore, the factors of -10 are: 1, -1, 2, -2, 5, -5, 10, and -10.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of -10 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
(-10 ÷ -1 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1
The prime factors of -10 are 2 and 5.
The prime factorization of -10 is: -1 × 2 × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, -10 is divided by -1 to get 10.
Step 2: Now divide 10 by 2 to get 5.
Step 3: Divide 5 by 5 to get 1. Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -10 is: -1 × 2 × 5.
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 10: (1, 10), (2, 5).
Negative factor pairs of -10: (-1, 10), (1, -10), (-2, 5), (2, -5).
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 5 people and 10 oranges. How will they share it equally?
Each person will get 2 oranges.
To divide the oranges equally, we need to divide the total oranges by the number of people.
10/5 = 2
A piece of rope is 10 meters long, and you need to cut it into 2 equal parts. How long will each piece be?
Each piece will be 5 meters long.
To find the length of each piece, divide the total length by 2.
10/2 = 5
There are 10 chairs and 2 tables. How many chairs will be around each table if they are equally distributed?
Each table will have 5 chairs.
To find how many chairs will be around each table, divide the total chairs by the number of tables.
10/2 = 5
In a party, there are 10 balloons and 5 children. How many balloons will each child get?
Each child will get 2 balloons.
Dividing the balloons by the total number of children, we will find the number of balloons each child gets.
10/5 = 2
10 plants need to be divided into 5 garden sections. How many plants will go in each section?
Each section will have 2 plants.
Divide the total number of plants by the number of sections.
10/5 = 2
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.