Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 828, how they are used in real life, and tips to learn them quickly.
The numbers that divide 828 evenly are known as factors of 828.
A factor of 828 is a number that divides the number without a remainder.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828.
Negative factors of 828: -1, -2, -3, -4, -6, -9, -12, -18, -23, -36, -46, -69, -92, -138, -207, -276, -414, and -828.
Prime factors of 828: 2, 3, and 23.
Prime factorization of 828: 2 × 2 × 3 × 3 × 23.
The sum of factors of 828: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 23 + 36 + 46 + 69 + 92 + 138 + 207 + 276 + 414 + 828 = 2175
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 828. Identifying the numbers which are multiplied to get the number 828 is the multiplication method.
Step 1: Multiply 828 by 1, 828 × 1 = 828.
Step 2: Check for other numbers that give 828 after multiplying
2 × 414 = 828
3 × 276 = 828
4 × 207 = 828
6 × 138 = 828
9 × 92 = 828
12 × 69 = 828
18 × 46 = 828
23 × 36 = 828
Therefore, the positive factor pairs of 828 are: (1, 828), (2, 414), (3, 276), (4, 207), (6, 138), (9, 92), (12, 69), (18, 46), (23, 36).
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 828 by 1, 828 ÷ 1 = 828.
Step 2: Continue dividing 828 by the numbers until the remainder becomes 0.
828 ÷ 1 = 828
828 ÷ 2 = 414
828 ÷ 3 = 276
828 ÷ 4 = 207
828 ÷ 6 = 138
828 ÷ 9 = 92
828 ÷ 12 = 69
828 ÷ 18 = 46
828 ÷ 23 = 36
Therefore, the factors of 828 are: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 828 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
828 ÷ 2 = 414
414 ÷ 2 = 207
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1
The prime factors of 828 are 2, 3, and 23.
The prime factorization of 828 is: 2 × 2 × 3 × 3 × 23.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 828 is divided by 2 to get 414.
Step 2: Now divide 414 by 2 to get 207.
Step 3: Then divide 207 by 3 to get 69.
Step 4: Divide 69 by 3 to get 23. Here, 23 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 828 is: 2 × 2 × 3 × 3 × 23.
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 828: (1, 828), (2, 414), (3, 276), (4, 207), (6, 138), (9, 92), (12, 69), (18, 46), (23, 36).
Negative factor pairs of 828: (-1, -828), (-2, -414), (-3, -276), (-4, -207), (-6, -138), (-9, -92), (-12, -69), (-18, -46), (-23, -36).
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 18 teams and 828 apples. How will they divide it equally?
They will get 46 apples each.
To divide the apples equally, we need to divide the total apples by the number of teams.
828/18 = 46
A garden is rectangular, the length of the garden is 69 meters and the total area is 828 square meters. Find the width?
12 meters.
To find the width of the garden, we use the formula, Area = length × width
828 = 69 × width
To find the value of width, we need to shift 69 to the left side.
828/69 = width
Width = 12.
There are 23 boxes and 828 candies. How many candies will be in each box?
Each box will have 36 candies.
To find the candies in each box, divide the total candies by the boxes.
828/23 = 36
In a stadium, there are 828 seats, and 12 rows. How many seats are there in each row?
There are 69 seats in each row.
Dividing the seats by the total rows, we will get the number of seats in each row.
828/12 = 69
828 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 92 books.
Divide total books by shelves.
828/9 = 92
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.