118 LearnersLast updated on May 26th, 2025
Factors of 825
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 825, how they are used in real life, and tips to learn them quickly.
What are the Factors of 825?
The numbers that divide 825 evenly are known as factors of 825.
A factor of 825 is a number that divides the number without a remainder.
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825.
Negative factors of 825: -1, -3, -5, -11, -15, -25, -33, -55, -75, -165, -275, and -825.
Prime factors of 825: 3, 5, and 11.
Prime factorization of 825: 3 × 52 × 11.
The sum of factors of 825: 1 + 3 + 5 + 11 + 15 + 25 + 33 + 55 + 75 + 165 + 275 + 825 = 1488
How to Find Factors of 825?
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 825. Identifying the numbers which are multiplied to get the number 825 is the multiplication method.
Step 1: Multiply 825 by 1, 825 × 1 = 825.
Step 2: Check for other numbers that give 825 after multiplying
3 × 275 = 825
5 × 165 = 825
11 × 75 = 825
15 × 55 = 825
25 × 33 = 825
Therefore, the positive factor pairs of 825 are: (1, 825), (3, 275), (5, 165), (11, 75), (15, 55), (25, 33).
All these factor pairs result in 825.
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 825 by 1, 825 ÷ 1 = 825.
Step 2: Continue dividing 825 by the numbers until the remainder becomes 0.
825 ÷ 1 = 825
825 ÷ 3 = 275
825 ÷ 5 = 165
825 ÷ 11 = 75
825 ÷ 15 = 55
825 ÷ 25 = 33
Therefore, the factors of 825 are: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
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 825 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
825 ÷ 3 = 275
275 ÷ 5 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
The prime factors of 825 are 3, 5, and 11.
The prime factorization of 825 is: 3 × 52 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 825 is divided by 3 to get 275.
Step 2: Now divide 275 by 5 to get 55.
Step 3: Then divide 55 by 5 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 825 is: 3 × 52 × 11.
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 825: (1, 825), (3, 275), (5, 165), (11, 75), (15, 55), and (25, 33).
Negative factor pairs of 825: (-1, -825), (-3, -275), (-5, -165), (-11, -75), (-15, -55), and (-25, -33).
Common Mistakes and How to Avoid Them in Factors of 825
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 825, 1 and 825 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 825 consist of -1, -3, -5, 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 2.5 as a factor because 825/2.5 = 330, 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 825 are prime numbers.
For example, 3, 5, and 11 are the prime factors of 825, but it has other factors like 15, 55.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, Not breaking 825 as 3 × 52 × 11 and missing all the key factors.
Factors of 825 Examples
Problem 1
There are 11 friends and 825 chocolates. How will they divide it equally?
They will get 75 chocolates each.
Explanation
To divide the chocolates equally, we need to divide the total chocolates with the number of friends.
825/11 = 75
Problem 2
A rectangular garden has a length of 15 meters and a total area of 825 square meters. Find the width.
55 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
825 = 15 × width
To find the value of width, we need to shift 15 to the left side.
825/15 = width
Width = 55.
Problem 3
There are 25 boxes and 825 apples. How many apples will be in each box?
Each box will have 33 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
825/25 = 33
Problem 4
In a school, there are 165 students, and they need to be arranged into 5 groups. How many students are there in each group?
There are 33 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
165/5 = 33
Problem 5
825 chairs need to be arranged in 15 rows. How many chairs will be in each row?
Each row will have 55 chairs.
Explanation
Divide total chairs with rows.
825/15 = 55
FAQs on Factors of 825
1.What are the factors of 825?
2.Mention the prime factors of 825.
3.Is 825 a multiple of 5?
4.Mention the factor pairs of 825.
5.What is the cube of 825?
Important Glossaries for Factor of 825
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 11 are prime factors of 825.
- 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 825 are (1, 825), (3, 275), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 825 is 3 × 52 × 11.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 825 is a multiple of 5.
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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.
