Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 822 apples and 6 baskets. How will they divide it equally?
They will get 137 apples each.
To divide the apples equally, we need to divide the total apples with the number of baskets.
822/6 = 137
A rectangular garden has a length of 137 meters and a total area of 822 square meters. Find the width?
6 meters.
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.
There are 3 teachers and 822 worksheets. How many worksheets will each teacher get?
Each teacher will get 274 worksheets.
To find the worksheets for each teacher, divide the total worksheets with the number of teachers.
822/3 = 274
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.
Dividing the participants with the total sessions, we will get the number of participants in each session.
822/2 = 411
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.
Divide the total books with the number of shelves.
822/1 = 822
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.
: She loves to read number jokes and games.