116 LearnersLast updated on May 26th, 2025
Factors of -26
Factors are the numbers that divide any given number evenly without 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 -26, how they are used in real life, and tips to learn them quickly.
What are the Factors of -26?
The numbers that divide -26 evenly are known as factors of -26.
A factor of -26 is a number that divides the number without remainder.
The factors of -26 are 1, 2, 13, and 26.
Negative factors of -26: -1, -2, -13, and -26.
Prime factors of -26: 2 and 13.
Prime factorization of -26: -1 × 2 × 13.
The sum of factors of -26: 1 + 2 + 13 + 26 = 42
How to Find Factors of -26?
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 -26. Identifying the numbers which are multiplied to get the number -26 is the multiplication method.
Step 1: Multiply -26 by 1, -26 × 1 = -26.
Step 2: Check for other numbers that give -26 after multiplying -1 × 26 = -26 -2 × 13 = -26
Therefore, the positive factor pairs of -26 are: (1, -26), (2, -13).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 -26 by 1, -26 ÷ 1 = -26.
Step 2: Continue dividing -26 by the numbers until the remainder becomes 0.
-26 ÷ 1 = -26
-26 ÷ 2 = -13
Therefore, the factors of -26 are: 1, 2, 13, 26.
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 -26 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-26 ÷ -1 = 26
26 ÷ 2 = 13
13 ÷ 13 = 1
The prime factors of -26 are 2 and 13.
The prime factorization of -26 is: -1 × 2 × 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, -26 is divided by -1 to get 26.
Step 2: Now divide 26 by 2 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -26 is: -1 × 2 × 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 -26: (1, -26), (2, -13).
Negative factor pairs of -26: (-1, 26), (-2, 13).
Common Mistakes and How to Avoid Them in Factors of -26
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 -26, 1 and -26 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 -26 consist of -1, -2, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -26/1.5 = -17.333, 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 -26 are prime numbers. For example, 2 and 13 are the prime factors of -26, but it has other factors like 1, 26.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -26 as -1 × 2 × 13 and missing all the key factors.
Factors of -26 Examples
Problem 1
There are 26 apples and 2 baskets. How will they divide them equally?
Each basket will have 13 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
26/2 = 13
Problem 2
A rectangular garden is divided into two equal sections, and its total area is 26 square meters. What is the area of each section?
13 square meters.
Explanation
To find the area of each section, divide the total area by the number of sections.
26/2 = 13
Problem 3
A box contains 26 candies and is divided equally among 13 children. How many candies will each child get?
Each child will get 2 candies.
Explanation
To find the number of candies each child gets, divide the total candies by the number of children.
26/13 = 2
Problem 4
In a class project, 26 sheets of paper are divided among 2 groups. How many sheets does each group receive?
Each group receives 13 sheets.
Explanation
Dividing the sheets by the number of groups, we will get the number of sheets each group receives.
26/2 = 13
Problem 5
A shipment of 26 boxes is split between 2 trucks. How many boxes will each truck carry?
Each truck will carry 13 boxes.
Explanation
Divide the total boxes by the number of trucks.
26/2 = 13
FAQs on Factors of -26
1.What are the factors of -26?
2.Mention the prime factors of -26.
3.Is -26 a multiple of 2?
4.Mention the factor pairs of -26?
5.What is the absolute value of -26?
Important Glossaries for Factor of -26
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -26 are 1, 2, 13, and 26.
- Prime factors: The factors which are prime numbers. For example, 2 and 13 are prime factors of -26.
- 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 -26 are (1, -26) and (2, -13).
- Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -26 is 26.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -13, and -26 are negative factors of -26.
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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.
