125 LearnersLast updated on May 26th, 2025
Factors of 1728
Factors are the numbers that divide any given number evenly without a 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 1728, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1728?
The numbers that divide 1728 evenly are known as factors of 1728.
A factor of 1728 is a number that divides the number without a remainder.
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 576, 864, and 1728.
Negative factors of 1728: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -96, -108, -144, -216, -288, -432, -576, -864, and -1728.
Prime factors of 1728: 2 and 3.
Prime factorization of 1728: 26 × 33.
The sum of factors of 1728: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 96 + 108 + 144 + 216 + 288 + 432 + 576 + 864 + 1728 = 5084.
How to Find Factors of 1728?
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 1728. Identifying the numbers which are multiplied to get the number 1728 is the multiplication method.
Step 1: Multiply 1728 by 1, 1728 × 1 = 1728.
Step 2: Check for other numbers that give 1728 after multiplying:
2 × 864 = 1728
3 × 576 = 1728
4 × 432 = 1728
6 × 288 = 1728
8 × 216 = 1728
9 × 192 = 1728
12 × 144 = 1728
16 × 108 = 1728
18 × 96 = 1728
24 × 72 = 1728
27 × 64 = 1728
32 × 54 = 1728
36 × 48 = 1728
Therefore, the positive factor pairs of 1728 are: (1, 1728), (2, 864), (3, 576), (4, 432), (6, 288), (8, 216), (9, 192), (12, 144), (16, 108), (18, 96), (24, 72), (27, 64), (32, 54), (36, 48).
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 1728 by 1, 1728 ÷ 1 = 1728.
Step 2: Continue dividing 1728 by the numbers until the remainder becomes 0.
1728 ÷ 1 = 1728
1728 ÷ 2 = 864
1728 ÷ 3 = 576
1728 ÷ 4 = 432
1728 ÷ 6 = 288
1728 ÷ 8 = 216
Therefore, the factors of 1728 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 576, 864, 1728.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1728 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
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 1728 are 2 and 3.
The prime factorization of 1728 is: 26 × 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, 1728 is divided by 2 to get 864.
Step 2: Now divide 864 by 2 to get 432.
Step 3: Then divide 432 by 2 to get 216.
Step 4: Divide 216 by 2 to get 108.
Step 5: Divide 108 by 2 to get 54.
Step 6: Divide 54 by 2 to get 27.
Step 7: Divide 27 by 3 to get 9.
Step 8: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 1728 is: 26 × 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 1728: (1, 1728), (2, 864), (3, 576), (4, 432), (6, 288), (8, 216), (9, 192), (12, 144), (16, 108), (18, 96), (24, 72), (27, 64), (32, 54), (36, 48).
Negative factor pairs of 1728: (-1, -1728), (-2, -864), (-3, -576), (-4, -432), (-6, -288), (-8, -216), (-9, -192), (-12, -144), (-16, -108), (-18, -96), (-24, -72), (-27, -64), (-32, -54), (-36, -48).
Common Mistakes and How to Avoid Them in Factors of 1728
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 1728, 1 and 1728 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 1728 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 1728/1.5 = 1152, 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 1728 are prime numbers.
For example, 2 and 3 are the prime factors of 1728, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1728 as 26 × 33 and missing all the key factors.
Factors of 1728 Examples
Problem 1
There are 6 teams and 1728 coins. How will they divide it equally?
They will get 288 coins each.
Explanation
To divide the coins equally, we need to divide the total coins by the number of teams.
1728/6 = 288
Problem 2
A storage box is cubic, with a volume of 1728 cubic centimeters. If the length of one edge is 12 cm, find the area of one face of the cube.
144 square centimeters.
Explanation
To find the area of one face of the cube, use the formula:
Area = edge × edge
Since the edge length is 12 cm,
Area = 12 × 12 = 144
Problem 3
There are 9 pallets and 1728 bricks. How many bricks will be on each pallet?
Each pallet will have 192 bricks.
Explanation
To find the bricks on each pallet, divide the total bricks by the number of pallets.
1728/9 = 192
Problem 4
A class has 1728 students, and they need to be divided into 16 groups. How many students are there in each group?
There are 108 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1728/16 = 108
Problem 5
1728 apples need to be packed into 18 crates. How many apples will go in each crate?
Each crate will have 96 apples.
Explanation
Divide the total apples by the crates.
1728/18 = 96
FAQs on Factors of 1728
1.What are the factors of 1728?
2.Mention the prime factors of 1728.
3.Is 1728 a multiple of 12?
4.Mention the factor pairs of 1728?
5.What is the cube root of 1728?
6.How can children in Canada use numbers in everyday life to understand Factors of 1728?
7.What are some fun ways kids in Canada can practice Factors of 1728 with numbers?
8.What role do numbers and Factors of 1728 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1728 skills?
Important Glossaries for Factors of 1728
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 576, 864, and 1728.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 1728.
- 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 1728 are (1, 1728), (2, 864), etc.
- Prime factorization: The process of expressing a number as a multiplication of its prime factors. For example, the prime factorization of 1728 is 26 × 33.
- Division method: A method to find factors by dividing a number by integers to see if the result is a whole number without a remainder. For example, when dividing 1728 by 6, the result is 288, which is a factor.
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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.
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