115 LearnersLast updated on May 26th, 2025
Factors of 1791
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 1791, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1791?
The numbers that divide 1791 evenly are known as factors of 1791.
A factor of 1791 is a number that divides the number without remainder.
The factors of 1791 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567, and 1791.
Negative factors of 1791: -1, -3, -7, -9, -21, -27, -63, -81, -189, -567, and -1791.
Prime factors of 1791: 3 and 7.
Prime factorization of 1791: 3 × 3 × 3 × 7 × 19.
The sum of factors of 1791: 1 + 3 + 7 + 9 + 21 + 27 + 63 + 81 + 189 + 567 + 1791 = 2759
How to Find Factors of 1791?
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 1791. Identifying the numbers which are multiplied to get the number 1791 is the multiplication method.
Step 1: Multiply 1791 by 1, 1791 × 1 = 1791.
Step 2: Check for other numbers that give 1791 after multiplying
3 × 597 = 1791
7 × 255 = 1791
9 × 199 = 1791
21 × 85 = 1791
27 × 67 = 1791
63 × 29 = 1791
Therefore, the positive factor pairs of 1791 are: (1, 1791), (3, 597), (7, 255), (9, 199), (21, 85), (27, 67), and (63, 29).
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 a simple division method -
Step 1: Divide 1791 by 1, 1791 ÷ 1 = 1791.
Step 2: Continue dividing 1791 by the numbers until the remainder becomes 0.
1791 ÷ 1 = 1791
1791 ÷ 3 = 597
1791 ÷ 7 = 255
1791 ÷ 9 = 199
1791 ÷ 21 = 85
1791 ÷ 27 = 67
1791 ÷ 63 = 29
Therefore, the factors of 1791 are: 1, 3, 7, 9, 21, 27, 63, 81, 189, 567, 1791.
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 1791 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1791 ÷ 3 = 597
597 ÷ 3 = 199
199 ÷ 3 = 67
67 ÷ 7 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 1791 are 3 and 7.
The prime factorization of 1791 is: 3 × 3 × 3 × 7 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1791 is divided by 3 to get 597.
Step 2: Now divide 597 by 3 to get 199.
Step 3: Then divide 199 by 3 to get 67.
Step 4: Divide 67 by 7 to get 9.
Step 5: Divide 9 by 3 to get 3.
Here, 3 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1791 is: 3 × 3 × 3 × 7 × 19.
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 1791: (1, 1791), (3, 597), (7, 255), (9, 199), (21, 85), (27, 67), and (63, 29).
Negative factor pairs of 1791: (-1, -1791), (-3, -597), (-7, -255), (-9, -199), (-21, -85), (-27, -67), and (-63, -29).
Common Mistakes and How to Avoid Them in Factors of 1791
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 1791, 1 and 1791 are also factors.
Factors of 1791 Examples
Problem 1
There are 9 friends and 1791 candies. How will they divide it equally?
They will get 199 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1791/9 = 199
Problem 2
A field is rectangular, the length of the field is 27 meters, and the total area is 1791 square meters. Find the width?
67 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1791 = 27 × width
To find the value of width, we need to shift 27 to the left side.
1791/27 = width
Width = 67.
Problem 3
There are 63 boxes and 1791 marbles. How many marbles will be in each box?
Each box will have 29 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
1791/63 = 29
Problem 4
In a class, there are 1791 students, and 9 groups. How many students are there in each group?
There are 199 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1791/9 = 199
Problem 5
1791 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 597 books.
Explanation
Divide total books by shelves.
1791/3 = 597
FAQs on Factors of 1791
1.What are the factors of 1791?
2.Mention the prime factors of 1791.
3.Is 1791 a multiple of 9?
4.Mention the factor pairs of 1791?
5.What is the square of 1791?
6.How can children in United States use numbers in everyday life to understand Factors of 1791?
7.What are some fun ways kids in United States can practice Factors of 1791 with numbers?
8.What role do numbers and Factors of 1791 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1791 skills?
Important Glossaries for Factor of 1791
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1791 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567, and 1791.
- Prime factors: The factors which are prime numbers. For example, 3 and 7 are prime factors of 1791.
- 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 1791 are (1, 1791), (3, 597), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 1791 is 3 × 3 × 3 × 7 × 19.
- Negative factors: Factors can also be negative. For example, the negative factors of 1791 are -1, -3, -7, 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.
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