100 LearnersLast updated on May 26th, 2025
Factors of 11664
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 11664, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 11664?
The numbers that divide 11664 evenly are known as factors of 11664.
A factor of 11664 is a number that divides the number without remainder.
The factors of 11664 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1458, 1944, 2916, 3888, 5832, and 11664.
Negative factors of 11664: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -36, -48, -54, -72, -81, -108, -162, -216, -243, -324, -486, -648, -972, -1458, -1944, -2916, -3888, -5832, and -11664.
Prime factors of 11664: 2 and 3.
Prime factorization of 11664: 2^6 × 3^6.
The sum of factors of 11664: This can be calculated by adding all the individual factors.
How to Find Factors of 11664?
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 11664. Identifying the numbers which are multiplied to get the number 11664 is the multiplication method.
Step 1: Multiply 11664 by 1, 11664 × 1 = 11664.
Step 2: Check for other numbers that give 11664 after multiplying
2 × 5832 = 11664
3 × 3888 = 11664
4 × 2916 = 11664
6 × 1944 = 11664
8 × 1458 = 11664
9 × 1296 = 11664
12 × 972 = 11664
16 × 729 = 11664
18 × 648 = 11664
24 × 486 = 11664
27 × 432 = 11664
36 × 324 = 11664
48 × 243 = 11664
54 × 216 = 11664
72 × 162 = 11664
81 × 144 = 11664
108 × 108 = 11664
Therefore, the positive factor pairs of 11664 are: (1, 11664), (2, 5832), (3, 3888), (4, 2916), (6, 1944), (8, 1458), (9, 1296), (12, 972), (16, 729), (18, 648), (24, 486), (27, 432), (36, 324), (48, 243), (54, 216), (72, 162), (81, 144), and (108, 108).
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 11664 by 1, 11664 ÷ 1 = 11664.
Step 2: Continue dividing 11664 by the numbers until the remainder becomes 0.
11664 ÷ 1 = 11664
11664 ÷ 2 = 5832
11664 ÷ 3 = 3888
11664 ÷ 4 = 2916
11664 ÷ 6 = 1944
11664 ÷ 8 = 1458
11664 ÷ 9 = 1296
11664 ÷ 12 = 972
11664 ÷ 16 = 729
11664 ÷ 18 = 648
11664 ÷ 24 = 486
11664 ÷ 27 = 432
11664 ÷ 36 = 324
11664 ÷ 48 = 243
11664 ÷ 54 = 216
11664 ÷ 72 = 162
11664 ÷ 81 = 144
11664 ÷ 108 = 108
Therefore, the factors of 11664 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1458, 1944, 2916, 3888, 5832, and 11664.
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 11664 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
11664 ÷ 2 = 5832
5832 ÷ 2 = 2916
2916 ÷ 2 = 1458
1458 ÷ 2 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 11664 are 2 and 3.
The prime factorization of 11664 is: 2^6 × 3^6.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 11664 is divided by 2 to get 5832.
Step 2: Now divide 5832 by 2 to get 2916.
Step 3: Then divide 2916 by 2 to get 1458.
Step 4: Divide 1458 by 2 to get 729.
Step 5: Divide 729 by 3 to get 243.
Step 6: Divide 243 by 3 to get 81.
Step 7: Divide 81 by 3 to get 27.
Step 8: Divide 27 by 3 to get 9.
Step 9: Divide 9 by 3 to get 3.
Step 10: Finally, 3 is divided by 3 to get 1.
Here, 2 and 3 are the smallest prime numbers, and they cannot be divided anymore.
So, the prime factorization of 11664 is: 2^6 × 3^6.
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 11664: (1, 11664), (2, 5832), (3, 3888), (4, 2916), (6, 1944), (8, 1458), (9, 1296), (12, 972), (16, 729), (18, 648), (24, 486), (27, 432), (36, 324), (48, 243), (54, 216), (72, 162), (81, 144), and (108, 108).
Negative factor pairs of 11664: (-1, -11664), (-2, -5832), (-3, -3888), (-4, -2916), (-6, -1944), (-8, -1458), (-9, -1296), (-12, -972), (-16, -729), (-18, -648), (-24, -486), (-27, -432), (-36, -324), (-48, -243), (-54, -216), (-72, -162), (-81, -144), and (-108, -108).
Common Mistakes and How to Avoid Them in Factors of 11664
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 11664, 1 and 11664 are also factors.
Factors of 11664 Examples
Problem 1
There are 36 students and 11664 pencils. How will they distribute it equally?
They will get 324 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils with the number of students.
11664/36 = 324
Problem 2
A dance floor is square, and the total area is 11664 square meters. What is the length of one side?
108 meters.
Explanation
To find the length of the side of the square dance floor, we find the square root of the area.
√11664 = 108
Problem 3
A company has 729 laptops and 11664 employees. How many laptops should each employee share?
Each employee will share 16 laptops.
Explanation
To find the number of laptops each employee will share, divide the total laptops with the number of employees.
11664/729 = 16
Problem 4
In a meeting, there are 486 participants and 11664 candies. How many candies will each participant receive?
Each participant will receive 24 candies.
Explanation
Dividing the candies by the number of participants, we will get the number of candies each will receive.
11664/486 = 24
Problem 5
A library has 972 books and needs to distribute them across 12 shelves. How many books will go on each shelf?
Each shelf will have 81 books.
Explanation
Divide total books with shelves.
972/12 = 81
FAQs on Factors of 11664
1.What are the factors of 11664?
2.Mention the prime factors of 11664.
3.Is 11664 a multiple of 9?
4.Mention the factor pairs of 11664.
5.What is the square root of 11664?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 11664?
7.What are some fun ways kids in Bahrain can practice Factors of 11664 with numbers?
8.What role do numbers and Factors of 11664 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 11664 skills?
Important Glossaries for Factors of 11664
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 11664 include 1, 2, 3, 4, 6, 8, 9, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 11664.
- 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 11664 include (1, 11664), (2, 5832), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 11664 is 2^6 × 3^6.
- Multiples: Numbers that are obtained by multiplying the original number with integers. For example, 11664 is a multiple of 9.
Explore More numbers
Previous to Factors of 11664
About BrightChamps in Bahrain
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.
