115 LearnersLast updated on May 26th, 2025
Factors of 29791
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 29791, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 29791?
The numbers that divide 29791 evenly are known as factors of 29791.
A factor of 29791 is a number that divides the number without remainder.
The factors of 29791 are 1, 17, 31, 527, 169, 29791.
Negative factors of 29791: -1, -17, -31, -527, -169, -29791.
Prime factors of 29791: 17 and 31.
Prime factorization of 29791: 17² × 31.
The sum of factors of 29791: 1 + 17 + 31 + 527 + 169 + 29791 = 30436
How to Find Factors of 29791?
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 29791. Identifying the numbers which are multiplied to get the number 29791 is the multiplication method.
Step 1: Multiply 29791 by 1, 29791 × 1 = 29791.
Step 2: Check for other numbers that give 29791 after multiplying
17 × 1753 = 29791
31 × 961 = 29791
Therefore, the positive factor pairs of 29791 are: (1, 29791), (17, 1753), (31, 961). All these factor pairs result in 29791. 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 29791 by 1, 29791 ÷ 1 = 29791.
Step 2: Continue dividing 29791 by the numbers until the remainder becomes 0.
29791 ÷ 1 = 29791
29791 ÷ 17 = 1753
29791 ÷ 31 = 961
Therefore, the factors of 29791 are: 1, 17, 31, 527, 169, 29791.
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 29791 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
29791 ÷ 17 = 1753
1753 ÷ 17 = 103
103 ÷ 31 = 3.
32258 The prime factors of 29791 are 17 and 31.
The prime factorization of 29791 is: 17² × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 29791 is divided by 17 to get 1753.
Step 2: Now divide 1753 by 17 to get 103.
Step 3: Then divide 103 by 31 to get 3.32258.
So, the prime factorization of 29791 is: 17² × 31.
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 29791: (1, 29791), (17, 1753), (31, 961)
Negative factor pairs of 29791: (-1, -29791), (-17, -1753), (-31, -961).
Common Mistakes and How to Avoid Them in Factors of 29791
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 29791, 1 and 29791 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 29791 include -1, -17, -31, etc.
Mistake 3
Including the Fraction
Sometimes fractions are mistakenly included as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 29791/1.5 ≈ 19860.67, 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 29791 are prime numbers. For example, 17 and 31 are the prime factors of 29791, but it has other factors like 527, 961, etc.
Mistake 5
Mistake in Factorization
People might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 29791 into 17² × 31 and missing all the key factors.
Factors of 29791 Examples
Problem 1
There are 17 friends and 29791 candies. How will they divide them equally?
They will get 1753 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
29791/17 = 1753
Problem 2
A field is rectangular, the length of the field is 31 meters and the total area is 29791 square meters. Find the width?
961 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
29791 = 31 × width
To find the value of width, we need to shift 31 to the left side.
29791/31 = width
Width = 961.
Problem 3
There are 527 bags and 29791 candies. How many candies will be in each bag?
Each bag will have 56 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
29791/527 = 56
Problem 4
In a class, there are 29791 students, and 31 groups. How many students are there in each group?
There are 961 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
29791/31 = 961
Problem 5
29791 books need to be arranged in 527 shelves. How many books will go on each shelf?
Each of the shelves has 56 books.
Explanation
Divide total books with shelves.
29791/527 = 56
FAQs on Factors of 29791
1.What are the factors of 29791?
2.Mention the prime factors of 29791.
3.Is 29791 a multiple of 17?
4.Mention the factor pairs of 29791?
5.What is the square of 29791?
6.How can children in Canada use numbers in everyday life to understand Factors of 29791?
7.What are some fun ways kids in Canada can practice Factors of 29791 with numbers?
8.What role do numbers and Factors of 29791 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 29791 skills?
Important Glossaries for Factor of 29791
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 29791 are 1, 17, 31, 527, 169, and 29791.
- Prime factors: The factors which are prime numbers. For example, 17 and 31 are prime factors of 29791.
- 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 29791 are (1, 29791), (17, 1753), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 29791 is 17² × 31.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find that 17 × 1753 = 29791.
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About BrightChamps in Canada
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.
