123 LearnersLast updated on May 26th, 2025
Factors of 1704
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.
What are the Factors of 1704?
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
How to Find Factors of 1704?
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 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.
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 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.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. 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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 1704
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
People 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 1704, 1 and 1704 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1704 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Sometimes fractions are mistakenly considered as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1704/1.5 does not result in 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 1704 are prime numbers. For instance, 2, 3, and 71 are the prime factors of 1704, but it has other factors like 4, 12, etc.
Mistake 5
Mistake in Factorization
People might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1704 as 23 × 3 × 71 and missing all the key factors.
Factors of 1704 Examples
Problem 1
There are 3 teachers and 1704 pencils. How will they divide them equally?
They will get 568 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of teachers.
1704/3 = 568
Problem 2
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.
Explanation
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.
Problem 3
There are 8 crates and 1704 apples. How many apples will be in each crate?
Each crate will have 213 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
1704/8 = 213
Problem 4
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.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
1704/12 = 142
Problem 5
1704 books need to be arranged on 24 shelves. How many books will go on each shelf?
Each of the shelves has 71 books.
Explanation
Divide total books by shelves.
1704/24 = 71
FAQs on Factors of 1704
1.What are the factors of 1704?
2.Mention the prime factors of 1704.
3.Is 1704 a multiple of 4?
4.Mention the factor pairs of 1704.
5.What is the square of 1704?
6.How can children in India use numbers in everyday life to understand Factors of 1704?
7.What are some fun ways kids in India can practice Factors of 1704 with numbers?
8.What role do numbers and Factors of 1704 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1704 skills?
Important Glossaries for Factors of 1704
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, 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.
- Prime factors: The factors that are prime numbers. For example, 2, 3, and 71 are prime factors of 1704.
- 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 1704 are (1, 1704), (2, 852), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For 1704, it is 23 × 3 × 71.
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to get the original number.
Explore More numbers
About BrightChamps in India
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.
