101 LearnersLast updated on May 26th, 2025
Factors of 966
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 966, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 966?
The numbers that divide 966 evenly are known as factors of 966.
A factor of 966 is a number that divides the number without remainder.
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 29, 42, 46, 58, 69, 87, 138, 161, 203, 322, 483, and 966.
Negative factors of 966: -1, -2, -3, -6, -7, -14, -21, -23, -29, -42, -46, -58, -69, -87, -138, -161, -203, -322, -483, and -966.
Prime factors of 966: 2, 3, 7, and 23.
Prime factorization of 966: 2 × 3 × 7 × 23.
The sum of factors of 966: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 29 + 42 + 46 + 58 + 69 + 87 + 138 + 161 + 203 + 322 + 483 + 966 = 2660
How to Find Factors of 966?
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 966. Identifying the numbers which are multiplied to get the number 966 is the multiplication method.
Step 1: Multiply 966 by 1, 966 × 1 = 966.
Step 2: Check for other numbers that give 966 after multiplying
2 × 483 = 966
3 × 322 = 966
6 × 161 = 966
7 × 138 = 966
14 × 69 = 966
21 × 46 = 966
23 × 42 = 966
29 × 33 = 966
Therefore, the positive factor pairs of 966 are: (1, 966), (2, 483), (3, 322), (6, 161), (7, 138), (14, 69), (21, 46), (23, 42), and (29, 33).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 966 by 1, 966 ÷ 1 = 966.
Step 2: Continue dividing 966 by the numbers until the remainder becomes 0.
966 ÷ 1 = 966
966 ÷ 2 = 483
966 ÷ 3 = 322
966 ÷ 6 = 161
966 ÷ 7 = 138
966 ÷ 14 = 69
966 ÷ 21 = 46
966 ÷ 23 = 42
966 ÷ 29 = 33
Therefore, the factors of 966 are: 1, 2, 3, 6, 7, 14, 21, 23, 29, 33, 42, 46, 69, 138, 161, 322, 483, 966.
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 966 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
966 ÷ 2 = 483
483 ÷ 3 = 161
161 ÷ 7 = 23
23 ÷ 23 = 1
The prime factors of 966 are 2, 3, 7, and 23. The prime factorization of 966 is: 2 × 3 × 7 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 966 is divided by 2 to get 483.
Step 2: Now divide 483 by 3 to get 161.
Step 3: Then divide 161 by 7 to get 23.
Here, 23 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 966 is: 2 × 3 × 7 × 23.
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 966: (1, 966), (2, 483), (3, 322), (6, 161), (7, 138), (14, 69), (21, 46), (23, 42), (29, 33).
Negative factor pairs of 966: (-1, -966), (-2, -483), (-3, -322), (-6, -161), (-7, -138), (-14, -69), (-21, -46), (-23, -42), (-29, -33).
Common Mistakes and How to Avoid Them in Factors of 966
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 966, 1 and 966 are also factors.
Factors of 966 Examples
Problem 1
A concert has 966 seats and 23 rows. How many seats are there in each row?
There are 42 seats in each row.
Explanation
To find the number of seats in each row, divide the total seats by the number of rows.
966/23 = 42
Problem 2
A park has a rectangular area of 966 square meters. If the length is 29 meters, what is the width?
The width is 33 meters.
Explanation
To find the width of the park, use the formula,
Area = length × width
966 = 29 × width
To find the width, divide the area by the length.
966/29 = width
Width = 33
Problem 3
A company has 966 employees and wants to create teams of 7. How many teams can they form?
They can form 138 teams.
Explanation
To find the number of teams, divide the total number of employees by the team size.
966/7 = 138
Problem 4
A library has 966 books and organizes them into 14 shelves. How many books are there on each shelf?
There are 69 books on each shelf.
Explanation
To find the number of books per shelf, divide the total books by the number of shelves.
966/14 = 69
Problem 5
A factory produces 966 units of a product in 3 days. How many units are produced per day?
322 units are produced per day.
Explanation
To calculate the daily production, divide the total units by the number of days.
966/3 = 322
FAQs on Factors of 966
1.What are the factors of 966?
2.Mention the prime factors of 966.
3.Is 966 a multiple of 7?
4.Mention the factor pairs of 966?
5.What is the square of 966?
6.How can children in Qatar use numbers in everyday life to understand Factors of 966?
7.What are some fun ways kids in Qatar can practice Factors of 966 with numbers?
8.What role do numbers and Factors of 966 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 966 skills?
Important Glossaries for Factor of 966
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 966 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 23 are prime factors of 966.
- 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 966 are (1, 966), (2, 483), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 966 = 2 × 3 × 7 × 23.
- Multiple: A number that can be divided by another number without a remainder. For example, 966 is a multiple of 3.
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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.
