121 LearnersLast updated on May 26th, 2025
Factors of 32768
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 32768, how they are used in real life, and tips to learn them quickly.
What are the Factors of 32768?
The numbers that divide 32768 evenly are known as factors of 32768.
A factor of 32768 is a number that divides the number without remainder.
The factors of 32768 include numbers like 1, 2, 4, 8, 16, 32, and others up to 32768.
Negative factors of 32768: -1, -2, -4, -8, -16, -32, and so forth up to -32768.
Prime factors of 32768: 2.
Prime factorization of 32768: 215.
The sum of factors of 32768 can be calculated by adding all the factors, but it is a complex calculation due to the large number of factors.
How to Find Factors of 32768?
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 32768. Identifying the numbers which are multiplied to get the number 32768 is the multiplication method.
Step 1: Multiply 32768 by 1, 32768 × 1 = 32768.
Step 2: Check for other numbers that give 32768 after multiplying:
2 × 16384 = 32768
4 × 8192 = 32768
8 × 4096 = 32768
16 × 2048 = 32768
Therefore, the positive factor pairs of 32768 are: (1, 32768), (2, 16384), (4, 8192), (8, 4096), (16, 2048), and so forth. 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 32768 by 1, 32768 ÷ 1 = 32768.
Step 2: Continue dividing 32768 by the numbers until the remainder becomes 0.
32768 ÷ 1 = 32768
32768 ÷ 2 = 16384
32768 ÷ 4 = 8192
32768 ÷ 8 = 4096
32768 ÷ 16 = 2048
Therefore, the factors of 32768 include: 1, 2, 4, 8, 16, 32, and others up to 32768.
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 32768 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
32768 ÷ 2 = 16384
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 factor of 32768 is 2.
The prime factorization of 32768 is: 2^15.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 32768 is divided by 2 to get 16384.
Step 2: Now divide 16384 by 2 to get 8192.
Step 3: Then divide 8192 by 2 to get 4096.
Step 4: Continue this process until you reach 1.
The prime factorization of 32768 is: 215.
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 32768: (1, 32768), (2, 16384), (4, 8192), and so forth.
Negative factor pairs of 32768: (-1, -32768), (-2, -16384), (-4, -8192), and so forth.
Common Mistakes and How to Avoid Them in Factors of 32768
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 32768, 1 and 32768 is also a factor.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 32768 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 32768/1.5 = 21845.333, 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 32768 are prime numbers. While 2 is the prime factor of 32768, it has other factors like 4, 16.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 32768 as 2^15 and missing all the key factors.
Factors of 32768 Examples
Problem 1
There are 32 teams participating in a tournament with 32768 participants. How many participants are in each team?
There will be 1024 participants in each team.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
32768/32 = 1024
Problem 2
A rectangular plot has a length of 16 meters and a total area of 32768 square meters. Find the width.
The width is 2048 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
32768 = 16 × width
To find the value of width, we need to shift 16 to the left side.
32768/16 = width
Width = 2048.
Problem 3
There are 256 boxes and 32768 marbles. How many marbles will be in each box?
Each box will have 128 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
32768/256 = 128
Problem 4
In a school, there are 32768 students, and they are divided into 1024 classes. How many students are there in each class?
There are 32 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
32768/1024 = 32
Problem 5
32768 pages need to be arranged in 128 volumes. How many pages will go in each volume?
Each volume will have 256 pages.
Explanation
Divide total pages by volumes.
32768/128 = 256
FAQs on Factors of 32768
1.What are the factors of 32768?
2.Mention the prime factors of 32768.
3.Is 32768 a multiple of 16?
4.Mention the factor pairs of 32768?
5.What is the square of 32768?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 32768?
7.What are some fun ways kids in Bahrain can practice Factors of 32768 with numbers?
8.What role do numbers and Factors of 32768 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 32768 skills?
Important Glossaries for Factors of 32768
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 32768 include 1, 2, 4, 8, 16, and others up to 32768.
- Prime factors: The factors which are prime numbers. For example, 2 is the prime factor of 32768.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 32768 is 215.
- 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 32768 include (1, 32768), (2, 16384), and others.
- Multiple: A multiple of a number is the result of multiplying that number by an integer. For example, 32768 is a multiple of 16.
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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.
