120 LearnersLast updated on May 26th, 2025
Factors of 3456
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 3456, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3456?
The numbers that divide 3456 evenly are known as factors of 3456.
A factor of 3456 is a number that divides the number without remainder.
The factors of 3456 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1152, 1728, and 3456.
Negative factors of 3456: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -96, -108, -144, -192, -216, -288, -432, -576, -864, -1152, -1728, -3456.
Prime factors of 3456: 2 and 3.
Prime factorization of 3456: 27 × 33.
The sum of factors of 3456: 10752.
How to Find Factors of 3456?
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 3456. Identifying the numbers which are multiplied to get the number 3456 is the multiplication method.
Step 1: Multiply 3456 by 1, 3456 × 1 = 3456.
Step 2: Check for other numbers that give 3456 after multiplying
2 × 1728 = 3456
3 × 1152 = 3456
4 × 864 = 3456
6 × 576 = 3456
8 × 432 = 3456
9 × 384 = 3456
12 × 288 = 3456
16 × 216 = 3456
18 × 192 = 3456
24 × 144 = 3456
27 × 128 = 3456
32 × 108 = 3456
36 × 96 = 3456
48 × 72 = 3456
Therefore, the positive factor pairs of 3456 are: (1, 3456), (2, 1728), (3, 1152), (4, 864), (6, 576), (8, 432), (9, 384), (12, 288), (16, 216), (18, 192), (24, 144), (27, 128), (32, 108), (36, 96), and (48, 72). All these factor pairs result in 3456. 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 3456 by 1, 3456 ÷ 1 = 3456.
Step 2: Continue dividing 3456 by numbers until the remainder becomes 0.
3456 ÷ 1 = 3456
3456 ÷ 2 = 1728
3456 ÷ 3 = 1152
3456 ÷ 4 = 864
3456 ÷ 6 = 576
3456 ÷ 8 = 432
3456 ÷ 9 = 384
3456 ÷ 12 = 288
3456 ÷ 16 = 216
3456 ÷ 18 = 192
3456 ÷ 24 = 144
3456 ÷ 27 = 128
3456 ÷ 32 = 108
3456 ÷ 36 = 96
3456 ÷ 48 = 72
Therefore, the factors of 3456 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1152, 1728, and 3456.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 3456 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3456 ÷ 2 = 1728
1728 ÷ 2 = 864
864 ÷ 2 = 432
432 ÷ 2 = 216
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 3456 are 2 and 3.
The prime factorization of 3456 is: 27 × 33.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3456 is divided by 2 to get 1728.
Step 2: Now divide 1728 by 2 to get 864.
Step 3: Then divide 864 by 2 to get 432.
Step 4: Divide 432 by 2 to get 216.
Step 5: Divide 216 by 2 to get 108.
Step 6: Divide 108 by 2 to get 54.
Step 7: Divide 54 by 2 to get 27.
Step 8: Divide 27 by 3 to get 9.
Step 9: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3456 is: 27 × 33.
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 3456: (1, 3456), (2, 1728), (3, 1152), (4, 864), (6, 576), (8, 432), (9, 384), (12, 288), (16, 216), (18, 192), (24, 144), (27, 128), (32, 108), (36, 96), (48, 72).
Negative factor pairs of 3456: (-1, -3456), (-2, -1728), (-3, -1152), (-4, -864), (-6, -576), (-8, -432), (-9, -384), (-12, -288), (-16, -216), (-18, -192), (-24, -144), (-27, -128), (-32, -108), (-36, -96), (-48, -72).
Common Mistakes and How to Avoid Them in Factors of 3456
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 3456, 1 and 3456 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 3456 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 3456/1.5 = 2304, 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 3456 are prime numbers.
For example, 2 and 3 are the prime factors of 3456, but it has other factors like 4, 6, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3456 as 27 × 33 and missing all the key factors.
Factors of 3456 Examples
Problem 1
There are 12 friends and 3456 candies. How will they divide them equally?
They will get 288 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
3456/12 = 288
Problem 2
A field is rectangular, the length of the field is 48 meters and the total area is 3456 square meters. Find the width?
72 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
3456 = 48 × width
To find the value of width, we need to shift 48 to the left side.
3456/48 = width
Width = 72.
Problem 3
There are 27 containers and 3456 liters of water. How many liters will be in each container?
Each container will have 128 liters.
Explanation
To find the liters in each container, divide the total liters with the containers.
3456/27 = 128
Problem 4
In a school, there are 3456 students, and 18 classes. How many students are there in each class?
There are 192 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
3456/18 = 192
Problem 5
3456 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each shelf will have 288 books.
Explanation
Divide total books by shelves.
3456/12 = 288
FAQs on Factors of 3456
1.What are the factors of 3456?
2.Mention the prime factors of 3456.
3.Is 3456 a multiple of 9?
4.Mention the factor pairs of 3456?
5.What is the square of 3456?
6.How can children in Qatar use numbers in everyday life to understand Factors of 3456?
7.What are some fun ways kids in Qatar can practice Factors of 3456 with numbers?
8.What role do numbers and Factors of 3456 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 3456 skills?
Important Glossaries for Factor of 3456
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3456 include 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 3456.
- 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 3456 are (1, 3456), (2, 1728), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 3456 is 27 × 33.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -3, etc., are negative factors of 3456.
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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.
