120 LearnersLast updated on May 26th, 2025
Factors of -169
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 -169, how they are used in real life, and tips to learn them quickly.
What are the Factors of -169?
The numbers that divide -169 evenly are known as factors of -169.
A factor of -169 is a number that divides the number without a remainder.
The factors of -169 are 1, -1, 13, -13, 169, and -169.
Prime factors of -169: 13.
Prime factorization of -169: -1 × 13 × 13.
The sum of the factors of -169: 1 - 1 + 13 - 13 + 169 - 169 = 0
How to Find Factors of -169?
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 pairs of numbers that are multiplied to give -169.
Identifying the numbers which are multiplied to get the number -169 is the multiplication method.
Step 1: Multiply -169 by 1, -169 × 1 = -169.
Step 2: Check for other numbers that give -169 after multiplying 13 × -13 = -169
Therefore, the factor pairs of -169 are (1, -169), (-1, 169), (13, -13), and (-13, 13).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors.
Factors can be calculated by following the simple division method
Step 1: Divide -169 by 1, -169 ÷ 1 = -169.
Step 2: Continue dividing -169 by the numbers until the remainder becomes 0.
-169 ÷ 1 = -169
-169 ÷ -1 = 169
-169 ÷ 13 = -13
-169 ÷ -13 = 13
Therefore, the factors of -169 are 1, -1, 13, -13, 169, and -169.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 -169 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-169 ÷ 13 = -13
-13 ÷ 13 = -1
The prime factors of -169 are 13.
The prime factorization of -169 is: -1 × 13 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, -169 is divided by 13 to get -13.
Step 2: Now divide -13 by 13 to get -1. Here, -1 is the smallest integer that cannot be divided anymore. So, the prime factorization of -169 is: -1 × 13 × 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 -169: (1, -169), and (13, -13).
Negative factor pairs of -169: (-1, 169), and (-13, 13).
Common Mistakes and How to Avoid Them in Factors of -169
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 -169, 1 and -169 is also a factor.
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 -169 include -1, -13, etc.
Mistake 3
Including Fractions
Children might sometimes mistakenly add fractions as factors. Only whole numbers can be factors.
For example, thinking 0.5 as a factor, because -169/0.5 = -338, 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 -169 are prime numbers.
For example, 13 is a prime factor of -169, but it has other factors like -1, -13.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -169 as -1 × 13 × 13 and missing key factors.
Factors of -169 Examples
Problem 1
A company has -169 units of a product to distribute equally among 13 departments. How many units does each department receive?
Each department receives -13 units.
Explanation
To distribute the products equally, we need to divide the total products by the number of departments.
-169/13 = -13
Problem 2
A rectangular field has a length of 13 meters, and its area is -169 square meters. What is the width of the field?
-13 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
-169 = 13 × width
To find the value of width, divide both sides by 13.
-169/13 = width
Width = -13.
Problem 3
A school has -169 books to distribute equally among 1 group. How many books will each group receive?
Each group will receive -169 books.
Explanation
To find the books in each group, divide the total books by the number of groups.
-169/1 = -169
Problem 4
A team has -169 points and 13 players. How many points does each player have?
Each player has -13 points.
Explanation
Dividing the points by the total players, we get the number of points for each player.
-169/13 = -13
Problem 5
A library has -169 books to arrange in 13 shelves. How many books will go on each shelf?
Each shelf will have -13 books.
Explanation
Divide the total books by the number of shelves.
-169/13 = -13
FAQs on Factors of -169
1.What are the factors of -169?
2.Mention the prime factors of -169.
3.Is -169 a multiple of 13?
4.Mention the factor pairs of -169?
5.Is -169 a perfect square?
Important Glossaries for Factor of -169
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -169 are 1, -1, 13, -13, 169, and -169.
- Prime factors: The factors that are prime numbers. For example, 13 is a prime factor of -169.
- 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 -169 are (1, -169) and (13, -13).
- Perfect square: A number that is the square of an integer. For example, -169 is a perfect square because it is the square of -13.
- Negative factors: Factors that are negative numbers, such as -1, -13, and -169 in the factors of -169.
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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.
