122 LearnersLast updated on May 26th, 2025
Factors of -156
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like dividing items equally, arranging things, etc. In this topic, we will learn about the factors of -156, how they are used in real life, and tips to learn them quickly.
What are the Factors of -156?
The numbers that divide -156 evenly are known as factors of -156.
A factor of -156 is a number that divides the number without leaving a remainder.
The positive factors of -156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.
Negative factors of -156: -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, and -156.
Prime factors of -156: 2, 3, and 13.
Prime factorization of -156: -1 × 2 × 2 × 3 × 13.
The sum of the positive factors of 156: 1 + 2 + 3 + 4 + 6 + 12 + 13 + 26 + 39 + 52 + 78 + 156 = 392.
How to Find Factors of -156?
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 -156. Identifying the numbers which are multiplied to get the number -156 is the multiplication method.
Step 1: Multiply -156 by 1, -156 × 1 = -156.
Step 2: Check for other numbers that give -156 after multiplying
2 × -78 = -156
3 × -52 = -156
4 × -39 = -156
6 × -26 = -156
12 × -13 = -156
Therefore, the positive factor pairs of -156 are: (1, -156), (2, -78), (3, -52), (4, -39), (6, -26), and (12, -13).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 -156 by 1, -156 ÷ 1 = -156.
Step 2: Continue dividing -156 by the numbers until the remainder becomes 0.
-156 ÷ 1 = -156
-156 ÷ 2 = -78
-156 ÷ 3 = -52
-156 ÷ 4 = -39
-156 ÷ 6 = -26
-156 ÷ 12 = -13
Therefore, the factors of -156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
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 -156 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-156 ÷ 2 = -78
-78 ÷ 2 = -39
-39 ÷ 3 = -13
-13 ÷ 13 = -1
The prime factors of -156 are 2, 3, and 13.
The prime factorization of -156 is: -1 × 2 × 2 × 3 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -156 is divided by 2 to get -78.
Step 2: Now divide -78 by 2 to get -39.
Step 3: Then divide -39 by 3 to get -13. Here, -13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of -156 is: -1 × 2 × 2 × 3 × 13.
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 -156: (1, -156), (2, -78), (3, -52), (4, -39), (6, -26), and (12, -13).
Negative factor pairs of -156: (-1, 156), (-2, 78), (-3, 52), (-4, 39), (-6, 26), and (-12, 13).
Common Mistakes and How to Avoid Them in Factors of -156
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -156, 1 and -156 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 -156 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because -156/1.5 = -104, 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 -156 are prime numbers.
For example, 2, 3, and 13 are the prime factors of -156, but it has other factors like 4, 6, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -156 as -1 × 2 × 2 × 3 × 13 and missing all the key factors.
Factors of -156 Examples
Problem 1
There are 12 apples and -156 grapes. How will they be divided equally among 13 baskets?
Each basket will have 1 apple and -12 grapes.
Explanation
To divide the apples and grapes equally, we need to divide the total number of apples and grapes by the number of baskets.
12/13 = 1 apple each -156/13 = -12 grapes each
Problem 2
A garden is rectangular, the length of the garden is 13 meters and the total area is -156 square meters. Find the width.
-12 meters.
Explanation
To find the width of the garden, we use the formula
Area = length × width
-156 = 13 × width
To find the value of width, we need to shift 13 to the left side.
-156/13 = width Width = -12.
Problem 3
There are 6 boxes and -156 marbles. How many marbles will be in each box?
Each box will have -26 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
-156/6 = -26
Problem 4
In an event, there are -156 chairs, and 39 rows. How many chairs are there in each row?
There are -4 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
-156/39 = -4
Problem 5
-156 chocolates need to be arranged in 13 shelves. How many chocolates will go on each shelf?
Each shelf will have -12 chocolates.
Explanation
Divide total chocolates by shelves.
-156/13 = -12
FAQs on Factors of -156
1.What are the factors of -156?
2.Mention the prime factors of -156.
3.Is -156 a multiple of 3?
4.Mention the factor pairs of -156.
5.What is the square of -156?
6.How can children in Qatar use numbers in everyday life to understand Factors of -156?
7.What are some fun ways kids in Qatar can practice Factors of -156 with numbers?
8.What role do numbers and Factors of -156 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -156 skills?
Important Glossaries for Factors of -156
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of -156.
- 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 -156 are (1, -156), (2, -78), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of -156 is -1 × 2 × 2 × 3 × 13.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of -156.
Explore More numbers
About BrightChamps in Qatar
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.
