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 -30, how they are used in real life, and tips to learn them quickly.
The numbers that divide -30 evenly are known as factors of -30.
A factor of -30 is a number that divides the number without a remainder.
The factors of -30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Negative factors of -30: -1, -2, -3, -5, -6, -10, -15, and -30.
Prime factors of -30: 2, 3, and 5.
Prime factorization of -30: -1 × 2 × 3 × 5.
The sum of the positive factors of 30: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72
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 -30. Identifying the numbers which are multiplied to get the number -30 is the multiplication method.
Step 1: Multiply -30 by -1, -30 × -1 = 30.
Step 2: Check for other numbers that give -30 after multiplying -2 × 15 = -30
-3 × 10 = -30
-5 × 6 = -30
Therefore, the positive factor pairs of -30 are: (1, 30), (2, 15), (3, 10), and (5, 6).
For every positive factor, there is a 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 -30 by 1, -30 ÷ 1 = -30.
Step 2: Continue dividing -30 by the numbers until the remainder becomes 0.
-30 ÷ 1 = -30
-30 ÷ 2 = -15
-30 ÷ 3 = -10
-30 ÷ 5 = -6
Therefore, the factors of -30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of -30 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
-30 ÷ -1 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of -30 are 2, 3, and 5.
The prime factorization of -30 is: -1 × 2 × 3 × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, -30 is divided by -1 to get 30.
Step 2: Now divide 30 by 2 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 -30 is: -1 × 2 × 3 × 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 -30: (1, 30), (2, 15), (3, 10), and (5, 6).
Negative factor pairs of -30: (-1, -30), (-2, -15), (-3, -10), and (-5, -6).
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 30 oranges and 5 baskets. How will they distribute them equally?
They will get 6 oranges in each basket.
To divide the oranges equally, we need to divide the total oranges by the number of baskets.
30/5 = 6
A rope is 30 meters long and needs to be cut into 3 equal parts. What will be the length of each part?
Each part will be 10 meters long.
To find the length of each part, divide the total length by the number of parts.
30/3 = 10
There are 10 students and 30 candies. How many candies will each student get?
Each student will get 3 candies.
To find the candies for each student, divide the total candies by the number of students.
30/10 = 3
A garden is divided into 5 sections. If the total area of the garden is 30 square meters, what is the area of each section?
Each section has an area of 6 square meters.
Dividing the total area by the number of sections gives the area of each section.
30/5 = 6
30 apples need to be packed into 6 bags. How many apples will go in each bag?
Each of the bags will have 5 apples.
Divide the total apples by the number of bags.
30/6 = 5
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.