120 LearnersLast updated on May 26th, 2025
Factors of 826
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 826, how they are used in real life, and tips to learn them quickly.
What are the Factors of 826?
The numbers that divide 826 evenly are known as factors of 826.
A factor of 826 is a number that divides the number without a remainder.
The factors of 826 are 1, 2, 413, and 826.
Negative factors of 826: -1, -2, -413, and -826.
Prime factors of 826: 2 and 413.
Prime factorization of 826: 2 × 413.
The sum of factors of 826: 1 + 2 + 413 + 826 = 1242.
How to Find Factors of 826?
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 826. Identifying the numbers which are multiplied to get the number 826 is the multiplication method.
Step 1: Multiply 826 by 1, 826 × 1 = 826.
Step 2: Check for other numbers that give 826 after multiplying
2 × 413 = 826
Therefore, the positive factor pairs of 826 are: (1, 826) and (2, 413).
All these factor pairs result in 826.
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 the simple division method
Step 1: Divide 826 by 1, 826 ÷ 1 = 826.
Step 2: Continue dividing 826 by the numbers until the remainder becomes 0.
826 ÷ 1 = 826
826 ÷ 2 = 413
Therefore, the factors of 826 are: 1, 2, 413, 826.
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 826 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
826 ÷ 2 = 413
413 is a prime number and cannot be divided further except by itself.
The prime factors of 826 are 2 and 413.
prime factorization of 826 is: 2 × 413.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 826 is divided by 2 to get 413.
Step 2: 413 is a prime number, so the factorization stops here. The prime factorization of 826 is: 2 × 413.
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 826: (1, 826) and (2, 413).
Negative factor pairs of 826: (-1, -826) and (-2, -413).
Common Mistakes and How to Avoid Them in Factors of 826
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
People 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 826, 1 and 826 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 826 include -1, -2, -413, etc.
Mistake 3
Including the Fraction
Sometimes people might incorrectly consider fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 826/1.5 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 826 are prime numbers.
For example, 2 and 413 are the prime factors of 826, but it also includes other factors like 1 and 826.
Mistake 5
Mistake in Factorization
People might skip steps in factorization and end up writing the wrong factors.
For example, not breaking 826 as 2 × 413 and missing all the key factors.
Factors of 826 Examples
Problem 1
There are 826 apples that need to be packed into boxes, with each box holding 2 apples. How many boxes are needed?
413 boxes are needed.
Explanation
To find the number of boxes, divide the total apples by the number of apples per box.
826/2 = 413
Problem 2
A swimming pool is rectangular, the length of the pool is 2 meters, and the total area is 826 square meters. Find the width.
413 meters.
Explanation
To find the width of the pool, we use the formula, Area = length × width
826 = 2 × width
To find the value of width, we need to shift 2 to the left side.
826/2 = width
Width = 413.
Problem 3
There are 826 marbles to be divided equally among 413 students. How many marbles will each student get?
Each student will get 2 marbles.
Explanation
To find the marbles each student gets, divide the total marbles by the number of students.
826/413 = 2
Problem 4
In a concert, there are 826 chairs arranged in rows of 2. How many rows are there?
There are 413 rows.
Explanation
Dividing the total chairs by the number of chairs per row, we will get the number of rows.
826/2 = 413
Problem 5
826 tiles need to be divided among 2 floors equally. How many tiles will go on each floor?
Each floor will have 413 tiles.
Explanation
Divide the total tiles by the number of floors.
826/2 = 413
FAQs on Factors of 826
1.What are the factors of 826?
2.Mention the prime factors of 826.
3.Is 826 a multiple of 2?
4.Mention the factor pairs of 826.
5.What is the square of 826?
Important Glossaries for Factors of 826
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 826 are 1, 2, 413, and 826.
- Prime factors: The factors which are prime numbers. For example, 2 and 413 are prime factors of 826.
- 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 826 are (1, 826) and (2, 413).
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 826 is 2 × 413.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -413, and -826 are negative factors of 826.
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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
: She loves to read number jokes and games.
