119 LearnersLast updated on May 26th, 2025
Factors of 822
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 822, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 822?
The numbers that divide 822 evenly are known as factors of 822.
A factor of 822 is a number that divides the number without remainder.
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, and 822.
Negative factors of 822: -1, -2, -3, -6, -137, -274, -411, and -822.
Prime factors of 822: 2, 3, and 137.
Prime factorization of 822: 2 × 3 × 137.
The sum of factors of 822: 1 + 2 + 3 + 6 + 137 + 274 + 411 + 822 = 1656
How to Find Factors of 822?
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 822. Identifying the numbers which are multiplied to get the number 822 is the multiplication method.
Step 1: Multiply 822 by 1, 822 × 1 = 822.
Step 2: Check for other numbers that give 822 after multiplying
2 × 411 = 822
3 × 274 = 822
6 × 137 = 822
Therefore, the positive factor pairs of 822 are: (1, 822), (2, 411), (3, 274), (6, 137).
All these factor pairs result in 822.
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 a simple division method
Step 1: Divide 822 by 1, 822 ÷ 1 = 822.
Step 2: Continue dividing 822 by the numbers until the remainder becomes 0.
822 ÷ 1 = 822
822 ÷ 2 = 411
822 ÷ 3 = 274
822 ÷ 6 = 137
Therefore, the factors of 822 are: 1, 2, 3, 6, 137, 274, 411, 822.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 822 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
822 ÷ 2 = 411
411 ÷ 3 = 137
137 ÷ 137 = 1
The prime factors of 822 are 2, 3, and 137.
The prime factorization of 822 is: 2 × 3 × 137.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 822 is divided by 2 to get 411.
Step 2: Now divide 411 by 3 to get 137. Here, 137 is a prime number and cannot be divided anymore. So, the prime factorization of 822 is: 2 × 3 × 137.
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 822: (1, 822), (2, 411), (3, 274), (6, 137).
Negative factor pairs of 822: (-1, -822), (-2, -411), (-3, -274), (-6, -137).
Common Mistakes and How to Avoid Them in Factors of 822
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 word. Always remember to include 1 and the number itself.
For example, in factors of 822, 1 and 822 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 822 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 822/1.5 = 548, 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 822 are prime numbers.
For example, 2, 3, and 137 are the prime factors of 822, but it has other factors like 6 and 411.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, Not breaking 822 as 2 × 3 × 137 and missing all the key factors.
Factors of 822 Examples
Problem 1
There are 822 apples and 6 baskets. How will they divide it equally?
They will get 137 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets.
822/6 = 137
Problem 2
A rectangular garden has a length of 137 meters and a total area of 822 square meters. Find the width?
6 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
822 = 137 × width
To find the value of width, we need to shift 137 to the left side.
822/137 = width
Width = 6.
Problem 3
There are 3 teachers and 822 worksheets. How many worksheets will each teacher get?
Each teacher will get 274 worksheets.
Explanation
To find the worksheets for each teacher, divide the total worksheets with the number of teachers.
822/3 = 274
Problem 4
In a conference, there are 822 participants, and 2 sessions. How many participants are there in each session?
There are 411 participants in each session.
Explanation
Dividing the participants with the total sessions, we will get the number of participants in each session.
822/2 = 411
Problem 5
822 books need to be arranged in 1 shelf. How many books will go on the shelf?
All 822 books will go on the shelf.
Explanation
Divide the total books with the number of shelves.
822/1 = 822
FAQs on Factors of 822
1.What are the factors of 822?
2.Mention the prime factors of 822.
3.Is 822 a multiple of 3?
4.Mention the factor pairs of 822?
5.What is the square of 822?
Important Glossaries for Factor of 822
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 822 are 1, 2, 3, 6, 137, 274, 411, and 822.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 137 are prime factors of 822.
- 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 822 are (1, 822), (2, 411), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For 822, it's 2 × 3 × 137.
- Multiple: A number that is the product of a given number and an integer. For instance, 822 is a multiple of 3.
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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.
