122 LearnersLast updated on May 26th, 2025
Factors of 816
Factors are the numbers that divide any given number evenly without 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 816, how they are used in real life, and tips to learn them quickly.
What are the Factors of 816?
The numbers that divide 816 evenly are known as factors of 816.
A factor of 816 is a number that divides the number without remainder.
The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, and 816.
Negative factors of 816: -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -48, -51, -68, -102, -136, -204, -272, -408, and -816.
Prime factors of 816: 2, 3, and 17.
Prime factorization of 816: (24 times 3 times 17).
The sum of factors of 816: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 48 + 51 + 68 + 102 + 136 + 204 + 272 + 408 + 816 = 2214
How to Find Factors of 816?
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 816. Identifying the numbers which are multiplied to get the number 816 is the multiplication method.
Step 1: Multiply 816 by 1, 816 × 1 = 816.
Step 2: Check for other numbers that give 816 after multiplying
2 × 408 = 816
3 × 272 = 816
4 × 204 = 816
6 × 136 = 816
8 × 102 = 816
12 × 68 = 816
17 × 48 = 816
24 × 34 = 816
Therefore, the positive factor pairs of 816 are: (1, 816), (2, 408), (3, 272), (4, 204), (6, 136), (8, 102), (12, 68), (17, 48), (24, 34).
All these factor pairs result in 816.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 816 by 1, 816 ÷ 1 = 816.
Step 2: Continue dividing 816 by the numbers until the remainder becomes 0.
816 ÷ 1 = 816
816 ÷ 2 = 408
816 ÷ 3 = 272
816 ÷ 4 = 204
816 ÷ 6 = 136
816 ÷ 8 = 102
816 ÷ 12 = 68
816 ÷ 17 = 48
816 ÷ 24 = 34
Therefore, the factors of 816 are: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816.
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 816 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
816 ÷ 2 = 408
408 ÷ 2 = 204
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 816 are 2, 3, and 17.
The prime factorization of 816 is: (24 times 3 times 17).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 816 is divided by 2 to get 408.
Step 2: Now divide 408 by 2 to get 204.
Step 3: Then divide 204 by 2 to get 102.
Step 4: Divide 102 by 2 to get 51.
Step 5: Divide 51 by 3 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 816 is: (24 times 3 times 17).
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 816: (1, 816), (2, 408), (3, 272), (4, 204), (6, 136), (8, 102), (12, 68), (17, 48), and (24, 34).
Negative factor pairs of 816: (-1, -816), (-2, -408), (-3, -272), (-4, -204), (-6, -136), (-8, -102), (-12, -68), (-17, -48), and (-24, -34).
Common Mistakes and How to Avoid Them in Factors of 816
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 816, 1 and 816 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 816 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 816/1.5 = 544, 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 816 are prime numbers.
For example, 2, 3, and 17 are the prime factors of 816, 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 816 as (24 times 3 times 17) and missing all the key factors.
Factors of 816 Examples
Problem 1
There are 12 teams and 816 points in a tournament. How will they divide them equally?
They will get 68 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
816/12 = 68
Problem 2
A rectangular garden has a length of 24 meters and a total area of 816 square meters. What is the width?
34 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
816 = 24 × width
To find the value of width, we need to shift 24 to the left side.
816/24 = width
Width = 34.
Problem 3
There are 34 boxes and 816 apples. How many apples will be in each box?
Each box will have 24 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
816/34 = 24
Problem 4
In a class, there are 816 students, and 68 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
816/68 = 12
Problem 5
816 books need to be arranged in 136 shelves. How many books will go on each shelf?
Each of the shelves has 6 books.
Explanation
Divide total books by shelves.
816/136 = 6
FAQs on Factors of 816
1.What are the factors of 816?
2.Mention the prime factors of 816.
3.Is 816 a multiple of 4?
4.Mention the factor pairs of 816?
5.What is the square of 816?
6.How can children in Thailand use numbers in everyday life to understand Factors of 816?
7.What are some fun ways kids in Thailand can practice Factors of 816 with numbers?
8.What role do numbers and Factors of 816 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 816 skills?
Important Glossaries for Factors of 816
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 816 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, and 816.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 816.
- 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 816 are (1, 816), (2, 408), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For instance, the prime factorization of 816 is (24 times 3 times 17).
- Negative factors: These are factors that are the negative counterparts of the positive factors. For example, the negative factors of 816 include -1, -2, -3, etc.
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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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