118 LearnersLast updated on May 26th, 2025
Factors of 823
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 823, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 823?
The numbers that divide 823 evenly are known as factors of 823.
A factor of 823 is a number that divides the number without remainder.
The factors of 823 are 1 and 823.
Negative factors of 823: -1 and -823.
Prime factors of 823: 823 (since 823 is a prime number).
The sum of factors of 823: 1 + 823 = 824
How to Find Factors of 823?
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 823. Since 823 is a prime number, it only has one multiplication pair:
Step 1: Multiply 823 by 1, 823 × 1 = 823.
Therefore, the positive factor pairs of 823 are: (1, 823).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by whole numbers until the remainder becomes zero helps list the numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 823 by 1, 823 ÷ 1 = 823.
Step 2: Since 823 is a prime number, no other numbers will divide it evenly.
Therefore, the factors of 823 are: 1 and 823.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: Since 823 is a prime number, the prime factorization of 823 is 823 itself.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. However, since 823 is a prime number, the factor tree is quite simple:
Step 1: 823 is already prime and cannot be broken down further. So, the prime factorization of 823 is: 823.
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 823: (1, 823).
Negative factor pairs of 823: (-1, -823).
Common Mistakes and How to Avoid Them in Factors of 823
Mistakes are common while finding factors. We can identify and correct these 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 823, 1 and 823 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 823 consist of -1 and -823.
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 823/1.5 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 823 are prime numbers is incorrect, but 823 itself is a prime number.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not recognizing 823 as a prime number and trying to break it down further.
Factors of 823 Examples
Problem 1
There are 823 marbles and 1 box. How many marbles will fit in each box?
All 823 marbles will fit in the box.
Explanation
To find out, divide the total number of marbles by the number of boxes.
823/1 = 823
Problem 2
A plot of land is square-shaped with an area of 823 square meters. What is the side length of the plot?
Since 823 is not a perfect square, the side length is not a whole number.
Explanation
For a square plot, side = √area.
√823 does not yield a whole number, so the side length is not a perfect integer.
Problem 3
You have 1 long ribbon of 823 meters. If you cut it into equal pieces, how many pieces will you get if each piece is 1 meter?
You will have 823 pieces.
Explanation
To find the number of pieces, divide the ribbon length by the piece length.
823/1 = 823
Problem 4
There are 823 participants in a marathon and each participant gets 1 bib number. How many bib numbers do you need?
You need 823 bib numbers.
Explanation
Each participant receives one bib number, so you need as many bib numbers as there are participants.
823 x 1 = 823
Problem 5
You have 823 stickers and want to distribute them equally among 823 friends. How many stickers will each friend get?
Each friend will get 1 sticker.
Explanation
To divide the stickers equally, divide the total number of stickers by the number of friends.
823/823 = 1
FAQs on Factors of 823
1.What are the factors of 823?
2.Mention the prime factors of 823.
3.Is 823 a prime number?
4.Mention the factor pairs of 823.
5.What is the square of 823?
Important Glossaries for Factors of 823
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 823 are 1 and 823.
- Prime factors: The factors which are prime numbers. For example, 823 is a prime factor of itself.
- 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 823 are (1, 823).
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 823 is a prime number.
- Perfect square: A number that is the square of an integer. For example, 823 is not a perfect square.
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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.
