116 LearnersLast updated on June 2nd, 2025
Factors of 3969
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 3969, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3969?
The numbers that divide 3969 evenly are known as factors of 3969.
A factor of 3969 is a number that divides the number without remainder.
The factors of 3969 include 1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1303, and 3969.
Negative factors of 3969: -1, -3, -9, -13, -27, -39, -81, -117, -169, -351, -507, -1303, and -3969.
Prime factors of 3969: 3 and 13.
Prime factorization of 3969: 34 × 132.
The sum of factors of 3969: 1 + 3 + 9 + 13 + 27 + 39 + 81 + 117 + 169 + 351 + 507 + 1303 + 3969 = 6589
How to Find Factors of 3969?
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 3969. Identifying the numbers which are multiplied to get the number 3969 is the multiplication method.
Step 1: Multiply 3969 by 1, 3969 × 1 = 3969.
Step 2: Check for other numbers that give 3969 after multiplying
3 × 1303 = 3969
9 × 441 = 3969
13 × 305 = 3969
27 × 147 = 3969
39 × 101 = 3969
Therefore, the positive factor pairs of 3969 are: (1, 3969), (3, 1303), (9, 441), (13, 305), (27, 147), (39, 101).
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 3969 by 1, 3969 ÷ 1 = 3969.
Step 2: Continue dividing 3969 by the numbers until the remainder becomes 0.
3969 ÷ 1 = 3969
3969 ÷ 3 = 1303
3969 ÷ 9 = 441
3969 ÷ 13 = 305
3969 ÷ 27 = 147
3969 ÷ 39 = 101
Therefore, the factors of 3969 are: 1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1303, and 3969.
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 3969 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3969 ÷ 3 = 1323
1323 ÷ 3 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 3969 are 3 and 13.
The prime factorization of 3969 is: 34 × 132.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 3969 is divided by 3 to get 1323.
Step 2: Now divide 1323 by 3 to get 441.
Step 3: Then divide 441 by 3 to get 147.
Step 4: Divide 147 by 3 to get 49.
Step 5: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3969 is: 34 × 132.
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 3969: (1, 3969), (3, 1303), (9, 441), (13, 305), (27, 147), and (39, 101).
Negative factor pairs of 3969: (-1, -3969), (-3, -1303), (-9, -441), (-13, -305), (-27, -147), and (-39, -101).
Common Mistakes and How to Avoid Them in Factors of 3969
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 3969, 1 and 3969 are also factors.
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 3969 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 3969/2.5 = 1587.6, 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 3969 are prime numbers.
For example, 3 and 13 are the prime factors of 3969, but it has other factors like 9, 81.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3969 as 34 × 132 and missing all the key factors.
Factors of 3969 Examples
Problem 1
There are 9 friends and 3969 marbles. How will they divide them equally?
They will get 441 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
3969/9 = 441
Problem 2
A garden is rectangular, the length of the garden is 27 meters and the total area is 3969 square meters. Find the width?
147 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
3969 = 27 × width
To find the value of width, we need to shift 27 to the left side.
3969/27 = width
Width = 147.
Problem 3
There are 13 bags and 3969 candies. How many candies will be in each bag?
Each bag will have 305 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
3969/13 = 305
Problem 4
In a class, there are 3969 students, and 27 groups. How many students are there in each group?
There are 147 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
3969/27 = 147
Problem 5
3969 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 1303 books.
Explanation
Divide total books by shelves.
3969/3 = 1303
FAQs on Factors of 3969
1.What are the factors of 3969?
2.Mention the prime factors of 3969.
3.Is 3969 a multiple of 9?
4.Mention the factor pairs of 3969?
5.What is the square root of 3969?
6.How can children in United States use numbers in everyday life to understand Factors of 3969?
7.What are some fun ways kids in United States can practice Factors of 3969 with numbers?
8.What role do numbers and Factors of 3969 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 3969 skills?
Important Glossaries for Factors of 3969
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3969 are 1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1303, and 3969.
- Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 3969.
- 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 3969 are (1, 3969), (3, 1303), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For instance, the prime factorization of 3969 is 34 × 132.
- Multiples: Numbers that can be divided by a particular number without leaving a remainder. For example, 3969 is a multiple of 9.
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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.
