123 LearnersLast updated on May 26th, 2025
Factors of 1724
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1724, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1724?
The numbers that divide 1724 evenly are known as factors of 1724.
A factor of 1724 is a number that divides the number without remainder.
The factors of 1724 are 1, 2, 4, 431, 862, and 1724.
Negative factors of 1724: -1, -2, -4, -431, -862, and -1724.
Prime factors of 1724: 2 and 431.
Prime factorization of 1724: 2 × 2 × 431.
The sum of factors of 1724: 1 + 2 + 4 + 431 + 862 + 1724 = 3024
How to Find Factors of 1724?
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 1724. Identifying the numbers which are multiplied to get the number 1724 is the multiplication method.
Step 1: Multiply 1724 by 1, 1724 × 1 = 1724.
Step 2: Check for other numbers that give 1724 after multiplying
2 × 862 = 1724
4 × 431 = 1724
Therefore, the positive factor pairs of 1724 are: (1, 1724), (2, 862), and (4, 431).
All these factor pairs result in 1724.
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 1724 by 1, 1724 ÷ 1 = 1724.
Step 2: Continue dividing 1724 by the numbers until the remainder becomes 0.
1724 ÷ 1 = 1724
1724 ÷ 2 = 862
1724 ÷ 4 = 431
Therefore, the factors of 1724 are: 1, 2, 4, 431, 862, and 1724.
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 factor tree
Using Prime Factorization: In this process, prime factors of 1724 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1724 ÷ 2 = 862
862 ÷ 2 = 431
431 ÷ 431 = 1
The prime factors of 1724 are 2 and 431.
The prime factorization of 1724 is: 2 × 2 × 431.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1724 is divided by 2 to get 862.
Step 2: Now divide 862 by 2 to get 431. Step 3: 431 is a prime number, so it cannot be divided further. So, the prime factorization of 1724 is: 2 × 2 × 431.
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 1724: (1, 1724), (2, 862), and (4, 431).
Negative factor pairs of 1724: (-1, -1724), (-2, -862), and (-4, -431).
Common Mistakes and How to Avoid Them in Factors of 1724
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1724, 1 and 1724 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 1724 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 1724/1.5 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 1724 are prime numbers.
For example, 2 and 431 are the prime factors of 1724, but it has other factors like 4, 862.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 1724 as 2 × 2 × 431 and missing all the key factors.
Factors of 1724 Examples
Problem 1
There are 431 students and 1724 pencils. How will they distribute them equally?
They will get 4 pencils each.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
1724/431 = 4
Problem 2
A rectangular billboard has a length of 862 meters and a total area of 1724 square meters. Find the width.
2 meters.
Explanation
To find the width of the billboard, we use the formula,
Area = length × width
1724 = 862 × width
To find the value of width, we need to shift 862 to the left side.
1724/862 = width
Width = 2.
Problem 3
There are 4 containers and 1724 marbles. How many marbles will be in each container?
Each container will have 431 marbles.
Explanation
To find the marbles in each container, divide the total marbles by the containers.
1724/4 = 431
Problem 4
In a class, there are 1724 students, and 431 groups. How many students are there in each group?
There are 4 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1724/431 = 4
Problem 5
1724 chairs need to be arranged in 2 rooms. How many chairs will go in each room?
Each of the rooms has 862 chairs.
Explanation
Divide total chairs by rooms.
1724/2 = 862
FAQs on Factors of 1724
1.What are the factors of 1724?
2.Mention the prime factors of 1724.
3.Is 1724 a multiple of 4?
4.Mention the factor pairs of 1724?
5.What is the square of 1724?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 1724?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 1724 with numbers?
8.What role do numbers and Factors of 1724 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 1724 skills?
Important Glossaries for Factor of 1724
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1724 are 1, 2, 4, 431, 862, and 1724.
- Prime factors: The factors which are prime numbers. For example, 2 and 431 are prime factors of 1724.
- 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 1724 are (1, 1724), (2, 862), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, 1724 can be prime factorized into 2 × 2 × 431.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to the target number. For example, using multiplication to find factors of 1724.
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About BrightChamps in Saudi Arabia
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.
