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 -90, how they are used in real life, and tips to learn them quickly.
The numbers that divide -90 evenly are known as factors of -90.
A factor of -90 is a number that divides the number without a remainder.
The factors of -90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Negative factors of -90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.
Prime factors of -90: 2, 3, and 5.
Prime factorization of -90: -1 × 2 × 3² × 5.
The sum of the positive factors of 90: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234.
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 -90. Identifying the numbers which are multiplied to get the number -90 is the multiplication method.
Step 1: Multiply -90 by 1, -90 × 1 = -90.
Step 2: Check for other numbers that give -90 after multiplying
2 × -45 = -90
-2 × 45 = -90
3 × -30 = -90
-3 × 30 = -90
5 × -18 = -90
-5 × 18 = -90
6 × -15 = -90
-6 × 15 = -90
9 × -10 = -90
-9 × 10 = -90
Therefore, the positive factor pairs of -90 are: (1, -90), (2, -45), (3, -30), (5, -18), (6, -15), and (9, -10).
For every positive factor, there is a corresponding negative factor.
Dividing the given numbers with 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 -90 by 1, -90 ÷ 1 = -90.
Step 2: Continue dividing -90 by the numbers until the remainder becomes 0.
-90 ÷ 1 = -90
-90 ÷ 2 = -45
-90 ÷ 3 = -30
-90 ÷ 5 = -18
-90 ÷ 6 = -15
-90 ÷ 9 = -10
Therefore, the factors of -90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
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 -90 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-90 ÷ -1 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of -90 are -1, 2, 3, and 5.
The prime factorization of -90 is: -1 × 2 × 3² × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 90 is divided by 2 to get 45.
Step 2: Now divide 45 by 3 to get 15.
Step 3: Then divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of -90 is: -1 × 2 × 3² × 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 -90: (1, -90), (2, -45), (3, -30), (5, -18), (6, -15), and (9, -10).
Negative factor pairs of -90: (-1, 90), (-2, 45), (-3, 30), (-5, 18), (-6, 15), and (-9, 10).
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 9 teams and -90 points to distribute. How will they distribute it equally?
They will distribute -10 points to each team.
To distribute the points equally, we need to divide the total points by the number of teams.
-90/9 = -10
A field is rectangular, the length of the field is 15 meters and the total area is -90 square meters. Find the width?
-6 meters.
To find the width of the field, we use the formula,
Area = length × width
-90 = 15 × width
To find the value of width, we need to shift 15 to the left side.
-90/15 = width
Width = -6.
There are 5 boxes and -90 marbles. How many marbles will be in each box?
Each box will have -18 marbles.
To find the marbles in each box, divide the total marbles by the boxes.
-90/5 = -18
In a class, there are -90 points to distribute, and 10 groups. How many points are distributed to each group?
Each group gets -9 points.
Dividing the points by the total groups, we will get the number of points each group gets.
-90/10 = -9
There are -90 plants to distribute in 6 gardens. How many plants will go in each garden?
Each garden will receive -15 plants.
Divide the total plants by the gardens.
-90/6 = -15
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.