100 LearnersLast updated on May 26th, 2025
Factors of -78
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 -78, how they are used in real life, and tips to learn them quickly.
What are the Factors of -78?
The numbers that divide -78 evenly are known as factors of -78.
A factor of -78 is a number that divides the number without a remainder.
The positive factors of -78 : 1, 2, 3, 6, 13, 26, 39, and 78.
The negative factors of -78: -1, -2, -3, -6, -13, -26, -39, and -78.
Prime factors of 78: 2, 3, and 13.
Prime factorization of 78: 2 × 3 × 13.
The sum of the positive factors of 78: 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 = 168
How to Find Factors of -78?
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 -78. Identifying the numbers which are multiplied to get the number -78 is the multiplication method.
Step 1: Multiply -78 by -1, -78 × -1 = 78.
Step 2: Check for other numbers that give -78 after multiplying
-2 × 39 = -78
-3 × 26 = -78
-6 × 13 = -78
Therefore, the positive factor pairs of 78 are: (1, 78), (2, 39), (3, 26), (6, 13)
. All these factor pairs result in 78.
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 in whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide -78 by -1, -78 ÷ -1 = 78.
Step 2: Continue dividing -78 by the numbers until the remainder becomes 0.
-78 ÷ -1 = 78
-78 ÷ -2 = 39
-78 ÷ -3 = 26
-78 ÷ -6 = 13
Therefore, the factors of -78 are: 1, 2, 3, 6, 13, 26, 39, 78, and their negatives.
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 78 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 78 are 2, 3, and 13.
The prime factorization of 78 is: 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, 78 is divided by 2 to get 39.
Step 2: Now divide 39 by 3 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 78 is: 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 78: (1, 78), (2, 39), (3, 26), (6, 13).
Negative factor pairs of -78: (-1, -78), (-2, -39), (-3, -26), (-6, -13).
Common Mistakes and How to Avoid Them in Factors of -78
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 -78, 1 and 78 are also factors.
Factors of -78 Examples
Problem 1
A group of 39 students has to split into teams of equal size. What is the maximum number of teams they can form if the total number of students is -78?
They can form 2 teams.
Explanation
To find the maximum number of teams, divide the total number of students by 39.
-78/39 = -2
Problem 2
A rectangular garden has a width of 13 meters, and the total area is -78 square meters. Find the length.
-6 meters.
Explanation
To find the length of the garden, use the formula, Area = length × width -78 = length × 13
To find the value of length, divide both sides by 13.
-78/13 = length
Length = -6.
Problem 3
A warehouse has 78 boxes, and they need to be packed in crates that can hold -3 boxes each. How many crates are needed?
26 crates are needed.
Explanation
To find the number of crates, divide the total boxes by the number each crate can hold.
78/3 = 26
Problem 4
A class has -78 chairs, and each row holds 6 chairs. How many rows are there?
There are 13 rows.
Explanation
Divide the total chairs by the number of chairs per row to find the number of rows.
-78/6 = -13
Problem 5
78 plants need to be arranged in a garden with 6 rows. How many plants will go in each row?
Each row will have 13 plants.
Explanation
Divide the total plants by rows.
78/6 = 13
FAQs on Factors of -78
1.What are the factors of -78?
2.Mention the prime factors of 78.
3.Is 78 a multiple of 2?
4.Mention the factor pairs of -78.
5.What is the square of 78?
6.How can children in Canada use numbers in everyday life to understand Factors of -78?
7.What are some fun ways kids in Canada can practice Factors of -78 with numbers?
8.What role do numbers and Factors of -78 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of -78 skills?
Important Glossaries for Factor of -78
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -78 are 1, 2, 3, 6, 13, 26, 39, 78, and their negatives.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 78.
- 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 -78 are (1, 78), (2, 39), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
- Division method: A method to find factors by dividing the original number by whole numbers until no remainder is left.
Explore More numbers
Previous to Factors of -78
About BrightChamps in Canada
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.
