Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 9 boxes and 3825 marbles. How will they divide it equally?
They will get 425 marbles each.
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
3825/9 = 425
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.
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.
There are 25 bins and 3825 apples. How many apples will be in each bin?
Each bin will have 153 apples.
To find the apples in each bin, divide the total apples by the bins.
3825/25 = 153
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.
Dividing the pieces by the total teams will give the number of pieces in each team.
3825/5 = 765
3825 books need to be arranged on 45 shelves. How many books will go on each shelf?
Each of the shelves has 85 books.
Divide total books by shelves.
3825/45 = 85
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.
: She loves to read number jokes and games.