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 1704, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1704 evenly are known as factors of 1704.
A factor of 1704 is a number that divides the number without remainder.
The factors of 1704 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 284, 426, 568, 852, and 1704.
Negative factors of 1704: -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, -284, -426, -568, -852, and -1704.
Prime factors of 1704: 2, 3, and 71.
Prime factorization of 1704: 23 × 3 × 71.
The sum of factors of 1704: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 + 284 + 426 + 568 + 852 + 1704 = 4503
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 1704. Identifying the numbers which are multiplied to get the number 1704 is the multiplication method.
Step 1: Multiply 1704 by 1, 1704 × 1 = 1704.
Step 2: Check for other numbers that give 1704 after multiplying:
2 × 852 = 1704
3 × 568 = 1704
4 × 426 = 1704
6 × 284 = 1704
8 × 213 = 1704
12 × 142 = 1704
17 × 100.235 (not a factor) Continue similarly with other divisors...
Therefore, the positive factor pairs of 1704 are: (1, 1704), (2, 852), (3, 568), (4, 426), (6, 284), (8, 213), (12, 142), (17, 100.235), (24, 71).
All these factor pairs result in 1704.
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 in whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 1704 by 1, 1704 ÷ 1 = 1704.
Step 2: Continue dividing 1704 by the numbers until the remainder becomes 0.
1704 ÷ 1 = 1704
1704 ÷ 2 = 852
1704 ÷ 3 = 568
1704 ÷ 4 = 426
1704 ÷ 6 = 284
1704 ÷ 8 = 213
1704 ÷ 12 = 142
1704 ÷ 17 = 100.235 (not a factor)
Therefore, the factors of 1704 are: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 284, 426, 568, 852, 1704.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1704 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1704 ÷ 2 = 852
852 ÷ 2 = 426
426 ÷ 2 = 213
213 ÷ 3 = 71
71 ÷ 71 = 1
The prime factors of 1704 are 2, 3, and 71.
The prime factorization of 1704 is: 23 × 3 × 71.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1704 is divided by 2 to get 852.
Step 2: Now divide 852 by 2 to get 426.
Step 3: Then divide 426 by 2 to get 213. Step 4: Divide 213 by 3 to get 71. Here, 71 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1704 is: 23 × 3 × 71.
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 1704: (1, 1704), (2, 852), (3, 568), (4, 426), (6, 284), (8, 213), (12, 142), (17, 100.235), (24, 71).
Negative factor pairs of 1704: (-1, -1704), (-2, -852), (-3, -568), (-4, -426), (-6, -284), (-8, -213), (-12, -142), (-17, -100.235), (-24, -71).
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 3 teachers and 1704 pencils. How will they divide them equally?
They will get 568 pencils each.
To divide the pencils equally, we need to divide the total pencils by the number of teachers.
1704/3 = 568
A garden is rectangular, the length of the garden is 24 meters and the total area is 1704 square meters. Find the width.
71 meters.
To find the width of the garden, we use the formula,
Area = length × width
1704 = 24 × width
To find the value of width, we need to shift 24 to the left side.
1704/24 = width
Width = 71.
There are 8 crates and 1704 apples. How many apples will be in each crate?
Each crate will have 213 apples.
To find the apples in each crate, divide the total apples by the crates.
1704/8 = 213
In a hall, there are 1704 chairs, and 12 rows. How many chairs are there in each row?
There are 142 chairs in each row.
Dividing the chairs by the total rows, we will get the number of chairs in each row.
1704/12 = 142
1704 books need to be arranged on 24 shelves. How many books will go on each shelf?
Each of the shelves has 71 books.
Divide total books by shelves.
1704/24 = 71
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.