Last updated on May 26th, 2025
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.
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.
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 12 friends and 3456 candies. How will they divide them equally?
They will get 288 candies each.
To divide the candies equally, we need to divide the total candies by the number of friends.
3456/12 = 288
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.
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.
There are 27 containers and 3456 liters of water. How many liters will be in each container?
Each container will have 128 liters.
To find the liters in each container, divide the total liters with the containers.
3456/27 = 128
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.
Dividing the students by the total classes, we will get the number of students in each class.
3456/18 = 192
3456 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each shelf will have 288 books.
Divide total books by shelves.
3456/12 = 288
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.
: She loves to read number jokes and games.