121 LearnersLast updated on May 26th, 2025
Factors of 1722
Factors are the numbers that divide any given number evenly without 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 1722, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1722?
The numbers that divide 1722 evenly are known as factors of 1722.
A factor of 1722 is a number that divides the number without remainder.
The factors of 1722 are 1, 2, 3, 6, 287, 574, 861, and 1722.
Negative factors of 1722: -1, -2, -3, -6, -287, -574, -861, and -1722.
Prime factors of 1722: 2, 3, and 287.
Prime factorization of 1722: 2 × 3 × 287.
The sum of factors of 1722: 1 + 2 + 3 + 6 + 287 + 574 + 861 + 1722 = 3456
How to Find Factors of 1722?
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 1722. Identifying the numbers which are multiplied to get the number 1722 is the multiplication method.
Step 1: Multiply 1722 by 1, 1722 × 1 = 1722.
Step 2: Check for other numbers that give 1722 after multiplying
2 × 861 = 1722
3 × 574 = 1722
6 × 287 = 1722
Therefore, the positive factor pairs of 1722 are: (1, 1722), (2, 861), (3, 574), (6, 287).
All these factor pairs result in 1722. 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 simple division method
Step 1: Divide 1722 by 1, 1722 ÷ 1 = 1722.
Step 2: Continue dividing 1722 by the numbers until the remainder becomes 0.
1722 ÷ 1 = 1722
1722 ÷ 2 = 861
1722 ÷ 3 = 574
1722 ÷ 6 = 287
Therefore, the factors of 1722 are: 1, 2, 3, 6, 287, 574, 861, 1722.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1722 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1722 ÷ 2 = 861
861 ÷ 3 = 287
287 ÷ 287 = 1
The prime factors of 1722 are 2, 3, and 287.
The prime factorization of 1722 is: 2 × 3 × 287.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1722 is divided by 2 to get 861.
Step 2: Now divide 861 by 3 to get 287.
Step 3: Divide 287 by 287 to get 1. So, the prime factorization of 1722 is: 2 × 3 × 287.
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 1722: (1, 1722), (2, 861), (3, 574), and (6, 287).
Negative factor pairs of 1722: (-1, -1722), (-2, -861), (-3, -574), and (-6, -287).
Common Mistakes and How to Avoid Them in Factors of 1722
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 1722, 1 and 1722 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 1722 consist of -1, -2, -3, 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 1722/1.5 = 1148, 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 1722 are prime numbers.
For example, 2, 3, and 287 are the prime factors of 1722, but it has other factors like 6, 861.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, Not breaking 1722 as 2 × 3 × 287 and missing all the key factors.
Factors of 1722 Examples
Problem 1
There are 3 tournament teams and 1722 points. How will they divide it equally?
They will get 574 points each.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
1722/3 = 574
Problem 2
A rectangular field has a length of 2 meters and a total area of 1722 square meters. Find the width.
861 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1722 = 2 × width
To find the value of width, we need to shift 2 to the left side.
1722/2 = width
Width = 861.
Problem 3
There are 6 containers and 1722 liters of water. How many liters will be in each container?
Each container will have 287 liters.
Explanation
To find the liters in each container, divide the total liters with the containers.
1722/6 = 287
Problem 4
In a class, there are 1722 students and 287 groups. How many students are there in each group?
There are 6 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1722/287 = 6
Problem 5
1722 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 574 books.
Explanation
Divide total books with shelves.
1722/3 = 574
FAQs on Factors of 1722
1.What are the factors of 1722?
2.Mention the prime factors of 1722.
3.Is 1722 a multiple of 6?
4.Mention the factor pairs of 1722?
5.What is the square of 1722?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1722?
7.What are some fun ways kids in United Kingdom can practice Factors of 1722 with numbers?
8.What role do numbers and Factors of 1722 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1722 skills?
Important Glossaries for Factor of 1722
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1722 are 1, 2, 3, 6, 287, 574, 861, and 1722.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 287 are prime factors of 1722.
- 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 1722 are (1, 1722), (2, 861), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1722 is 2 × 3 × 287.
- Negative factors: The negative counterparts of positive factors. For example, -1, -2, -3, -6, etc., are negative factors of 1722.
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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.
Fun Fact
: She loves to read number jokes and games.
