102 LearnersLast updated on May 26th, 2025
Factors of -66
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 -66, how they are used in real life, and tips to learn them quickly.
What are the Factors of -66?
The numbers that divide -66 evenly are known as factors of -66.
A factor of -66 is a number that divides the number without remainder.
The factors of -66 are 1, 2, 3, 6, 11, 22, 33, and 66.
Negative factors of -66: -1, -2, -3, -6, -11, -22, -33, and -66.
Prime factors of -66: 2, 3, and 11.
Prime factorization of -66: -1 × 2 × 3 × 11.
The sum of factors of 66 (ignoring the negative sign): 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 = 144
How to Find Factors of -66?
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 -66. Identifying the numbers which are multiplied to get the number -66 is the multiplication method.
Step 1: Multiply -66 by -1, -66 × -1 = 66.
Step 2: Check for other numbers that give -66 after multiplying
-2 × 33 = -66
-3 × 22 = -66
-6 × 11 = -66
Therefore, the positive factor pairs of -66 are: (1, 66), (2, 33), (3, 22), (6, 11).
All these factor pairs result in 66 or -66.
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 -66 by -1, -66 ÷ -1 = 66.
Step 2: Continue dividing -66 by the numbers until the remainder becomes 0.
-66 ÷ -1 = 66
-66 ÷ -2 = 33
-66 ÷ -3 = 22
-66 ÷ -6 = 11
Therefore, the factors of -66 are: 1, 2, 3, 6, 11, 22, 33, 66.
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 -66 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of -66 are 2, 3, and 11.
The prime factorization of -66 is: -1 × 2 × 3 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 66 is divided by 2 to get 33.
Step 2: Now divide 33 by 3 to get 11.
Step 3: Then divide 11 by 11 to get 1. So, the prime factorization of -66 is: -1 × 2 × 3 × 11.
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 -66: (1, 66), (2, 33), (3, 22), (6, 11).
Negative factor pairs of -66: (-1, -66), (-2, -33), (-3, -22), (-6, -11).
Common Mistakes and How to Avoid Them in Factors of -66
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
People 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 -66, 1 and 66 are also factors.
Factors of -66 Examples
Problem 1
There are 6 teams and -66 points to be distributed equally. How will they distribute it?
Each team will receive -11 points.
Explanation
To distribute the points equally, divide the total points by the number of teams.
-66/6 = -11
Problem 2
A rectangular plot has a length of 11 meters and an area of 66 square meters. Find the width?
6 meters.
Explanation
To find the width of the plot, use the formula, Area = length × width 66 = 11 × width
To find the value of width, divide 66 by 11.
66/11 = width
Width = 6.
Problem 3
There are 3 boxes and -66 items. How many items will be in each box?
Each box will have -22 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
-66/3 = -22
Problem 4
In a class, there are -66 candies, and 11 students. How many candies are there for each student?
Each student receives -6 candies.
Explanation
Dividing the candies by the number of students, we get the number of candies each student receives.
-66/11 = -6
Problem 5
-66 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each shelf will have -11 books.
Explanation
Divide total books by the number of shelves.
-66/6 = -11
FAQs on Factors of -66
1.What are the factors of -66?
2.Mention the prime factors of -66.
3.Is 66 a multiple of 3?
4.Mention the factor pairs of -66?
5.What is the square of 66?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of -66?
7.What are some fun ways kids in United Kingdom can practice Factors of -66 with numbers?
8.What role do numbers and Factors of -66 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of -66 skills?
Important Glossaries for Factors of -66
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -66 are 1, 2, 3, 6, 11, 22, 33, and 66.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of -66.
- 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 -66 are (1, 66), (2, 33), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of -66.
- Prime factorization: The process of breaking down a number into its prime factors. For example, -66 can be expressed as -1 × 2 × 3 × 11 in prime factorization.
Explore More numbers
Previous to Factors of -66
About BrightChamps in United Kingdom
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.
