118 LearnersLast updated on May 26th, 2025
Factors of -30
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.
What are the Factors of -30?
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
How to Find Factors of -30?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 -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.
Finding Factors Using Division Method
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.
Prime Factors and Prime Factorization
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
- Using factor tree
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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of -30
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 -30, 1 and 30 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -30 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -30/1.5 = -20, 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 -30 are prime numbers.
For example, 2, 3, and 5 are the prime factors of -30, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -30 as -1 × 2 × 3 × 5 and missing all the key factors.
Factors of -30 Examples
Problem 1
There are 30 oranges and 5 baskets. How will they distribute them equally?
They will get 6 oranges in each basket.
Explanation
To divide the oranges equally, we need to divide the total oranges by the number of baskets.
30/5 = 6
Problem 2
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.
Explanation
To find the length of each part, divide the total length by the number of parts.
30/3 = 10
Problem 3
There are 10 students and 30 candies. How many candies will each student get?
Each student will get 3 candies.
Explanation
To find the candies for each student, divide the total candies by the number of students.
30/10 = 3
Problem 4
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.
Explanation
Dividing the total area by the number of sections gives the area of each section.
30/5 = 6
Problem 5
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.
Explanation
Divide the total apples by the number of bags.
30/6 = 5
FAQs on Factors of -30
1.What are the factors of -30?
2.Mention the prime factors of -30.
3.Is 30 a multiple of 5?
4.Mention the factor pairs of -30.
5.What is the square of 30?
6.How can children in India use numbers in everyday life to understand Factors of -30?
7.What are some fun ways kids in India can practice Factors of -30 with numbers?
8.What role do numbers and Factors of -30 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -30 skills?
Important Glossaries for Factor of -30
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -30 are 1, 2, 3, 5, 6, 10, 15, and 30.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of -30.
- 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 -30 are (1, 30), (2, 15), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of -30.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of -30 is -1 × 2 × 3 × 5.
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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
: She loves to read number jokes and games.
