115 LearnersLast updated on May 26th, 2025
Factors of 1788
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 1788, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1788?
The numbers that divide 1788 evenly are known as factors of 1788.
A factor of 1788 is a number that divides the number without remainder.
The factors of 1788 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 459, 594, 1788.
Negative factors of 1788: -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, -459, -594, -1788.
Prime factors of 1788: 2, 3, 17.
Prime factorization of 1788: 2 × 3^2 × 17.
The sum of factors of 1788: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 17 + 18 + 34 + 36 + 51 + 68 + 102 + 153 + 204 + 306 + 459 + 594 + 1788 = 3868
How to Find Factors of 1788?
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 1788. Identifying the numbers which are multiplied to get the number 1788 is the multiplication method.
Step 1: Multiply 1788 by 1, 1788 × 1 = 1788.
Step 2: Check for other numbers that give 1788 after multiplying
2 × 894 = 1788
3 × 596 = 1788
4 × 447 = 1788
6 × 298 = 1788
9 × 198 = 1788
12 × 149 = 1788
17 × 105 = 1788
18 × 99 = 1788
34 × 52 = 1788
36 × 49.666 (not a factor)
51 × 35.058 (not a factor)
Therefore, the positive factor pairs of 1788 include: (1, 1788), (2, 894), (3, 596), (4, 447), (6, 298), (9, 198), (12, 149), (17, 105), (18, 99), (34, 52).
All these factor pairs result in 1788.
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 the simple division method -
Step 1: Divide 1788 by 1, 1788 ÷ 1 = 1788.
Step 2: Continue dividing 1788 by the numbers until the remainder becomes 0.
1788 ÷ 1 = 1788
1788 ÷ 2 = 894
1788 ÷ 3 = 596
1788 ÷ 4 = 447
188 ÷ 6 = 298
1788 ÷ 9 = 198
1788 ÷ 12 = 149
1788 ÷ 17 = 105
1788 ÷ 18 = 99
Therefore, the factors of 1788 are: 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 459, 594, 1788.
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 1788 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1788 ÷ 2 = 894
894 ÷ 2 = 447
447 ÷ 3 = 149
149 ÷ 17 = 1
The prime factors of 1788 are 2, 3, and 17.
The prime factorization of 1788 is: 2 × 3^2 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1788 is divided by 2 to get 894.
Step 2: Now divide 894 by 2 to get 447.
Step 3: Then divide 447 by 3 to get 149.
Step 4: Divide 149 by 17 to get 1.
Here, 17 is the smallest prime number and cannot be divided anymore.
So, the prime factorization of 1788 is: 2 × 3^2 × 17.
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 1788: (1, 1788), (2, 894), (3, 596), (4, 447), (6, 298), (9, 198), (12, 149), (17, 105), (18, 99), (34, 52).
Negative factor pairs of 1788: (-1, -1788), (-2, -894), (-3, -596), (-4, -447), (-6, -298), (-9, -198), (-12, -149), (-17, -105), (-18, -99), (-34, -52).
Common Mistakes and How to Avoid Them in Factors of 1788
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 1788, 1 and 1788 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1788 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1788/1.5 = 1192, which 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 1788 are prime numbers.
For example, 2, 3, and 17 are the prime factors of 1788, but it has other factors like 4, 6, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1788 as 2 × 3^2 × 17 and missing all the key factors.
Factors of 1788 Examples
Problem 1
There are 6 groups and 1788 apples. How will they distribute it equally?
Each group will get 298 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of groups.
1788/6 = 298
Problem 2
A rectangular garden has a width of 34 meters and a total area of 1788 square meters. Find the length.
52 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1788 = length × 34
To find the value of length, we need to shift 34 to the left side.
1788/34 = length
Length = 52.
Problem 3
A teacher has 1788 pencils and wants to distribute them equally among 17 students. How many pencils will each student receive?
Each student will receive 105 pencils.
Explanation
To find the pencils each student will receive, divide the total pencils by the number of students.
1788/17 = 105
Problem 4
There are 1788 chairs to be arranged in 9 rows. How many chairs will be in each row?
198 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
1788/9 = 198
Problem 5
1788 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each shelf will have 149 books.
Explanation
Divide total books by shelves.
1788/12 = 149
FAQs on Factors of 1788
1.What are the factors of 1788?
2.Mention the prime factors of 1788.
3.Is 1788 a multiple of 4?
4.Mention the factor pairs of 1788?
5.What is the square of 1788?
6.How can children in India use numbers in everyday life to understand Factors of 1788?
7.What are some fun ways kids in India can practice Factors of 1788 with numbers?
8.What role do numbers and Factors of 1788 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1788 skills?
Important Glossaries for Factors of 1788
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1788 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 1788.
- 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 1788 are (1, 1788), (2, 894), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1788 is 2 × 3^2 × 17.
- Multiples: Numbers that can be obtained by multiplying a number by integers. For example, 1788 is a multiple of 894, 596, etc.
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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
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