119 LearnersLast updated on May 26th, 2025
Factors of 824
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 824, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 824?
The numbers that divide 824 evenly are known as factors of 824.
A factor of 824 is a number that divides the number without remainder.
The factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824.
Negative factors of 824: -1, -2, -4, -8, -103, -206, -412, and -824.
Prime factors of 824: 2 and 103.
Prime factorization of 824: (23 times 103).
The sum of factors of 824: 1 + 2 + 4 + 8 + 103 + 206 + 412 + 824 = 1560
How to Find Factors of 824?
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 824. Identifying the numbers which are multiplied to get the number 824 is the multiplication method.
Step 1: Multiply 824 by 1, 824 × 1 = 824.
Step 2: Check for other numbers that give 824 after multiplying
2 × 412 = 824
4 × 206 = 824
8 × 103 = 824
Therefore, the positive factor pairs of 824 are: (1, 824), (2, 412), (4, 206), (8, 103).
All these factor pairs result in 824.
For every positive factor, there is a 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 824 by 1, 824 ÷ 1 = 824.
Step 2: Continue dividing 824 by the numbers until the remainder becomes 0.
824 ÷ 1 = 824
824 ÷ 2 = 412
824 ÷ 4 = 206
824 ÷ 8 = 103
Therefore, the factors of 824 are: 1, 2, 4, 8, 103, 206, 412, and 824.
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 824 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
824 ÷ 2 = 412
412 ÷ 2 = 206
206 ÷ 2 = 103
103 ÷ 103 = 1
The prime factors of 824 are 2 and 103.
The prime factorization of 824 is: (23 times 103).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 824 is divided by 2 to get 412.
Step 2: Now divide 412 by 2 to get 206.
Step 3: Then divide 206 by 2 to get 103. Here, 103 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 824 is: \(2^3 \times 103\).
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 824: (1, 824), (2, 412), (4, 206), and (8, 103).
Negative factor pairs of 824: (-1, -824), (-2, -412), (-4, -206), and (-8, -103).
Common Mistakes and How to Avoid Them in Factors of 824
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 824, 1 and 824 is also a factor.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 824 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 824/1.5 = 549.333, 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 824 are prime numbers.
For instance, 2 and 103 are the prime factors of 824, but it has other factors like 4, 206.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 824 as (23 times 103) and missing all the key factors.
Factors of 824 Examples
Problem 1
There are 8 teams and 824 points. How will the points be divided equally among the teams?
Each team will get 103 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
824/8 = 103
Problem 2
A garden is rectangular, the length of the garden is 206 meters and the total area is 824 square meters. Find the width.
4 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
824 = 206 × width
To find the value of width, we need to shift 206 to the left side.
824/206 = width
Width = 4.
Problem 3
There are 206 bags and 824 apples. How many apples will be in each bag?
Each bag will have 4 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
824/206 = 4
Problem 4
In a concert, there are 824 seats and 4 sections. How many seats are there in each section?
There are 206 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
824/4 = 206
Problem 5
824 books need to be arranged in 8 bookshelves. How many books will go on each shelf?
Each of the bookshelves has 103 books.
Explanation
Divide total books by shelves.
824/8 = 103
FAQs on Factors of 824
1.What are the factors of 824?
2.Mention the prime factors of 824.
3.Is 824 a multiple of 4?
4.Mention the factor pairs of 824?
5.What is the square of 824?
6.How can children in Australia use numbers in everyday life to understand Factors of 824?
7.What are some fun ways kids in Australia can practice Factors of 824 with numbers?
8.What role do numbers and Factors of 824 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 824 skills?
Important Glossaries for Factor of 824
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824.
- Prime factors: The factors which are prime numbers. For example, 2 and 103 are prime factors of 824.
- 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 824 are (1, 824), (2, 412), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 824 is (23 times 103).
- Negative factors: Factors that are negative counterparts of the positive factors. For example, -1, -2, -4, and -8 are negative factors of 824.
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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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