Last updated on May 26th, 2025
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.
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.
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 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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
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 6 teams and 1728 coins. How will they divide it equally?
They will get 288 coins each.
To divide the coins equally, we need to divide the total coins by the number of teams.
1728/6 = 288
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.
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
There are 9 pallets and 1728 bricks. How many bricks will be on each pallet?
Each pallet will have 192 bricks.
To find the bricks on each pallet, divide the total bricks by the number of pallets.
1728/9 = 192
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.
Dividing the students by the total groups, we will get the number of students in each group.
1728/16 = 108
1728 apples need to be packed into 18 crates. How many apples will go in each crate?
Each crate will have 96 apples.
Divide the total apples by the crates.
1728/18 = 96
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.