100 LearnersLast updated on May 26th, 2025
Factors of 16384
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 16384, how they are used in real life, and tips to learn them quickly.
What are the Factors of 16384?
The numbers that divide 16384 evenly are known as factors of 16384.
A factor of 16384 is a number that divides the number without remainder.
The factors of 16384 include powers of 2 since 16384 is a power of 2.
Negative factors of 16384: These are simply the negative of its positive factors.
Prime factors of 16384: 2.
Prime factorization of 16384: 2^14.
The sum of factors of 16384: This would require calculating the sum of all its factors, which depends on its factorization.
How to Find Factors of 16384?
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 16384.
Identifying the numbers which are multiplied to get the number 16384 is the multiplication method.
Since 16384 is a power of 2, many of its factors are powers of 2.
Finding Factors Using Division Method
Dividing the given numbers with 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 the simple division method.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 16384 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
16384 ÷ 2 = 8192
8192 ÷ 2 = 4096
4096 ÷ 2 = 2048
2048 ÷ 2 = 1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
The prime factorization of 16384 is: 2^14.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 16384 is divided by 2 to get 8192.
Step 2: Now divide 8192 by 2 to get 4096.
Continue this process until you reach 1, as shown in the prime factorization steps above.
The prime factorization of 16384 is: 2^14.
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 16384: (1, 16384), (2, 8192), etc., involving powers of 2.
Negative factor pairs of 16384: (-1, -16384), (-2, -8192), etc.
Common Mistakes and How to Avoid Them in Factors of 16384
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 16384, 1 and 16384 are also factors.
Factors of 16384 Examples
Problem 1
There are 16384 apples and 128 baskets. How many apples will go in each basket if divided equally?
Each basket will have 128 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
16384/128 = 128
Problem 2
A rectangular piece of land has a length of 64 meters, and the total area is 16384 square meters. Find the width.
256 meters.
Explanation
To find the width of the land, we use the formula,
Area = length × width
16384 = 64 × width
To find the value of width, divide 16384 by 64.
16384/64 = width
Width = 256.
Problem 3
There are 256 houses, and each house needs the same number of tiles. If there are 16384 tiles in total, how many tiles will each house receive?
Each house will receive 64 tiles.
Explanation
To find the tiles for each house, divide the total tiles by the number of houses.
16384/256 = 64
Problem 4
In a school, there are 16 buses, and a total of 16384 students need to be transported. How many students will be in each bus?
Each bus will have 1024 students.
Explanation
Dividing the students by the total buses, we will get the number of students in each bus.
16384/16 = 1024
Problem 5
16384 books need to be arranged on 128 shelves. How many books will go on each shelf?
Each shelf will have 128 books.
Explanation
Divide total books by shelves.
16384/128 = 128
FAQs on Factors of 16384
1.What are the factors of 16384?
2.Mention the prime factors of 16384.
3.Is 16384 a multiple of 4?
4.Mention the factor pairs of 16384.
5.What is the square root of 16384?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 16384?
7.What are some fun ways kids in United Kingdom can practice Factors of 16384 with numbers?
8.What role do numbers and Factors of 16384 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 16384 skills?
Important Glossaries for Factor of 16384
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 16384 are powers of 2.
- Prime factors: The factors which are prime numbers. For example, 2 is the prime factor of 16384.
- 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 16384 are (1, 16384), (2, 8192), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 16384 is 2^14.
- Powers of 2: Numbers that are results of raising 2 to an integer power, such as 2, 4, 8, etc.
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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.
