119 LearnersLast updated on May 26th, 2025
Factors of 828
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.
What are the Factors of 828?
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
How to Find Factors of 828?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 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.
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 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.
Prime Factors and Prime Factorization
The factors can be found by dividing it with 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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 828
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 828, 1 and 828 are also factors.
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 828 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 828/1.5 = 552, 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 828 are prime numbers.
For example, 2, 3, and 23 are the prime factors of 828, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 828 as 2 × 2 × 3 × 3 × 23 and missing all the key factors.
Factors of 828 Examples
Problem 1
There are 18 teams and 828 apples. How will they divide it equally?
They will get 46 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams.
828/18 = 46
Problem 2
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.
Explanation
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.
Problem 3
There are 23 boxes and 828 candies. How many candies will be in each box?
Each box will have 36 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
828/23 = 36
Problem 4
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.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
828/12 = 69
Problem 5
828 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 92 books.
Explanation
Divide total books by shelves.
828/9 = 92
FAQs on Factors of 828
1.What are the factors of 828?
2.Mention the prime factors of 828.
3.Is 828 a multiple of 9?
4.Mention the factor pairs of 828?
5.What is the square of 828?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 828?
7.What are some fun ways kids in Indonesia can practice Factors of 828 with numbers?
8.What role do numbers and Factors of 828 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 828 skills?
Important Glossaries for Factors of 828
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 23 are prime factors of 828.
- 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 828 are (1, 828), (2, 414), etc.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 828 is a multiple of 9.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 828 is 2 × 2 × 3 × 3 × 23.
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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
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