121 LearnersLast updated on May 26th, 2025
Factors of 3825
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 3825, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3825?
The numbers that divide 3825 evenly are known as factors of 3825.
A factor of 3825 is a number that divides the number without a remainder.
The factors of 3825 are 1, 3, 5, 9, 15, 25, 45, 75, 1275, and 3825.
Negative factors of 3825: -1, -3, -5, -9, -15, -25, -45, -75, -1275, and -3825.
Prime factors of 3825: 3 and 5.
Prime factorization of 3825: 3 × 3 × 5 × 5 × 17.
The sum of factors of 3825: 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 1275 + 3825 = 5278
How to Find Factors of 3825?
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 3825. Identifying the numbers which are multiplied to get the number 3825 is the multiplication method.
Step 1: Multiply 3825 by 1, 3825 × 1 = 3825.
Step 2: Check for other numbers that give 3825 after multiplying
3 × 1275 = 3825
5 × 765 = 3825
9 × 425 = 3825
15 × 255 = 3825
25 × 153 = 3825
45 × 85 = 3825
75 × 51 = 3825
Therefore, the positive factor pairs of 3825 are: (1, 3825), (3, 1275), (5, 765), (9, 425), (15, 255), (25, 153), (45, 85), (75, 51). 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 a simple division method -
Step 1: Divide 3825 by 1, 3825 ÷ 1 = 3825.
Step 2: Continue dividing 3825 by the numbers until the remainder becomes 0.
3825 ÷ 1 = 3825
3825 ÷ 3 = 1275
3825 ÷ 5 = 765
3825 ÷ 9 = 425
3825 ÷ 15 = 255
3825 ÷ 25 = 153
3825 ÷ 45 = 85
3825 ÷ 75 = 51
Therefore, the factors of 3825 are: 1, 3, 5, 9, 15, 25, 45, 75, 1275, 3825.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 3825 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.
3825 ÷ 3 = 1275
1275 ÷ 3 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 3825 are 3, 5, and 17.
The prime factorization of 3825 is: 3 × 3 × 5 × 5 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3825 is divided by 3 to get 1275.
Step 2: Now divide 1275 by 3 to get 425.
Step 3: Then divide 425 by 5 to get 85.
Step 4: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 3825 is: 3 × 3 × 5 × 5 × 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 3825: (1, 3825), (3, 1275), (5, 765), (9, 425), (15, 255), (25, 153), (45, 85), (75, 51).
Negative factor pairs of 3825: (-1, -3825), (-3, -1275), (-5, -765), (-9, -425), (-15, -255), (-25, -153), (-45, -85), (-75, -51).
Common Mistakes and How to Avoid Them in Factors of 3825
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 word. Always remember to include 1 and the number itself.
For example, in factors of 3825, 1 and 3825 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 3825 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 3825/2.5 = 1530, 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 3825 are prime numbers.
For example, 3 and 5 are the prime factors of 3825, but it has other factors like 9, 25.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3825 as 3 × 3 × 5 × 5 × 17 and missing key factors.
Factors of 3825 Examples
Problem 1
There are 9 boxes and 3825 marbles. How will they divide it equally?
They will get 425 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
3825/9 = 425
Problem 2
A garden is rectangular; the length of the garden is 15 meters and the total area is 3825 square meters. Find the width?
255 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
3825 = 15 × width
To find the value of width, we need to shift 15 to the left side.
3825/15 = width
Width = 255.
Problem 3
There are 25 bins and 3825 apples. How many apples will be in each bin?
Each bin will have 153 apples.
Explanation
To find the apples in each bin, divide the total apples by the bins.
3825/25 = 153
Problem 4
In a workshop, there are 3825 pieces of wood, and 5 teams. How many pieces are there in each team?
There are 765 pieces in each team.
Explanation
Dividing the pieces by the total teams will give the number of pieces in each team.
3825/5 = 765
Problem 5
3825 books need to be arranged on 45 shelves. How many books will go on each shelf?
Each of the shelves has 85 books.
Explanation
Divide total books by shelves.
3825/45 = 85
FAQs on Factors of 3825
1.What are the factors of 3825?
2.Mention the prime factors of 3825.
3.Is 3825 a multiple of 9?
4.Mention the factor pairs of 3825?
5.What is the square of 3825?
6.How can children in India use numbers in everyday life to understand Factors of 3825?
7.What are some fun ways kids in India can practice Factors of 3825 with numbers?
8.What role do numbers and Factors of 3825 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 3825 skills?
Important Glossaries for Factors of 3825
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3825 are 1, 3, 5, 9, 15, 25, 45, 75, 1275, and 3825.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 17 are prime factors of 3825.
- 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 3825 are (1, 3825), (3, 1275), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, 3825 = 3 × 3 × 5 × 5 × 17.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number. For example, finding the factors of 3825 using multiplication pairs.
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About BrightChamps in India
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.
