122 LearnersLast updated on May 26th, 2025
Factors of 827
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 827, how they are used in real life, and tips to learn them quickly.
What are the Factors of 827?
The numbers that divide 827 evenly are known as factors of 827.
A factor of 827 is a number that divides the number without remainder.
The factors of 827 are 1 and 827.
Negative factors of 827: -1 and -827.
Since 827 is a prime number, it has no prime factors other than itself.
The prime factorization of 827 is simply 827.
The sum of factors of 827: 1 + 827 = 828
How to Find Factors of 827?
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 827. For a prime number like 827, the only multiplication pair is:
Step 1: Multiply 827 by 1, 827 × 1 = 827.
Therefore, the only positive factor pair of 827 is: (1, 827).
For every positive factor, there is a corresponding negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 827 by 1, 827 ÷ 1 = 827.
Step 2: Continue dividing 827 by the numbers until the remainder becomes 0.
827 ÷ 1 = 827
Since 827 is a prime number, dividing by any number other than 1 and 827 results in a remainder.
Therefore, the factors of 827 are: 1 and 827.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 827 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
Since 827 is a prime number, it cannot be broken down further.
The prime factorization of 827 is simply 827.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. In the case of 827, since it is a prime number, the factor tree is quite simple:
Step 1: 827 is a prime number and cannot be divided further. So, the prime factorization of 827 is simply 827.
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 827: (1, 827).
Negative factor pairs of 827: (-1, -827).
Common Mistakes and How to Avoid Them in Factors of 827
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 827, 1 and 827 are 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 827 include -1 and -827.
Mistake 3
Including the Fraction
Children might sometimes mistakenly include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor is incorrect, because 827/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 827 are prime. While 827 is a prime number, 1 is also a factor but not 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 that 827 is itself a prime number and cannot be broken down further.
Factors of 827 Examples
Problem 1
There are 2 teams and 827 apples. How will they divide it equally?
They cannot divide the apples equally without a remainder.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams. Since 827 is a prime number, dividing by any number other than 1 or 827 will leave a remainder.
Problem 2
A company has 827 chairs and wants to distribute them equally among 5 offices. How many chairs will each office receive?
Each office will receive 165 chairs with 2 chairs remaining.
Explanation
To divide the chairs equally, we divide the total number of chairs by the number of offices.
827 ÷ 5 = 165 R2
Problem 3
There are 827 students and 3 buses. How many students will be on each bus?
Each bus will have 275 students with 2 students remaining.
Explanation
To find the number of students on each bus, divide the total students by the number of buses.
827 ÷ 3 = 275 R2
Problem 4
An estate agent has 827 houses and wants to allocate them equally among 7 managers. How many houses will each manager get?
Each manager will get 118 houses with 1 house remaining.
Explanation
To allocate the houses equally, we divide the total number of houses by the number of managers.
827 ÷ 7 = 118 R1
Problem 5
A library has 827 books that need to be distributed evenly across 4 sections. How many books will each section have?
Each section will have 206 books with 3 books remaining.
Explanation
Divide the total books by the number of sections.
827 ÷ 4 = 206 R3
FAQs on Factors of 827
1.What are the factors of 827?
2.Is 827 a prime number?
3.Is 827 a multiple of 3?
4.Mention the factor pairs of 827?
5.What is the square of 827?
Important Glossaries for Factors of 827
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 827 are 1 and 827.
- Prime factors: The factors which are prime numbers. For example, 827 itself is a prime factor since 827 is a prime number.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 827 is (1, 827).
- Prime number: A number that has only two distinct factors: 1 and itself. For example, 827 is a prime number.
- Remainder: The amount left over after division when a number cannot be evenly divided. For example, dividing 827 by any number other than 1 or 827 results in a remainder.
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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.
