Last updated on May 26th, 2025
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 1025, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1025 evenly are known as factors of 1025.
A factor of 1025 is a number that divides the number without remainder.
The factors of 1025 are 1, 5, 25, 41, 205, and 1025.
-1, -5, -25, -41, -205, and -1025.
Prime factors of 1025: 5 and 41.
Prime factorization of 1025: 5 × 205 = 5 × (5 × 41).
The sum of factors of 1025: 1 + 5 + 25 + 41 + 205 + 1025 = 1302
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 1025. Identifying the numbers which are multiplied to get the number 1025 is the multiplication method.
Step 1: Multiply 1025 by 1, 1025 × 1 = 1025.
Step 2: Check for other numbers that give 1025 after multiplying
5 × 205 = 1025
25 × 41 = 1025
Therefore, the positive factor pairs of 1025 are: (1, 1025), (5, 205), (25, 41). All these factor pairs result in 1025. For every positive factor, there is a negative factor.
Dividing the given numbers with the 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 1025 by 1, 1025 ÷ 1 = 1025.
Step 2: Continue dividing 1025 by the numbers until the remainder becomes 0.
1025 ÷ 1 = 1025
1025 ÷ 5 = 205
1025 ÷ 25 = 41
Therefore, the factors of 1025 are: 1, 5, 25, 41, 205, 1025.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1025 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1025 ÷ 5 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1
The prime factors of 1025 are 5 and 41.
The prime factorization of 1025 is: 5 × 5 × 41.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1025 is divided by 5 to get 205.
Step 2: Now divide 205 by 5 to get 41.
Step 3: Here, 41 is a prime number, so it cannot be divided further. So, the prime factorization of 1025 is: 5 × 5 × 41.
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 1025: (1, 1025), (5, 205), (25, 41).
Negative factor pairs of 1025: (-1, -1025), (-5, -205), (-25, -41).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A concert hall has 1025 seats. If each row has 25 seats, how many rows are there?
There will be 41 rows.
To find the number of rows, divide the total number of seats by the number of seats per row.
1025/25 = 41
A bookstore has 1025 books to arrange equally on 5 shelves. How many books will each shelf have?
Each shelf will have 205 books.
To find the number of books per shelf, divide the total books by the number of shelves.
1025/5 = 205
A farmer has 1025 apples and wants to pack them into boxes, each containing 205 apples. How many boxes does he need?
The farmer needs 5 boxes.
To find the number of boxes needed, divide the total apples by the number of apples per box.
1025/205 = 5
A school has 1025 students participating in an event. If each group can have 41 students, how many groups can be formed?
There will be 25 groups.
To find the number of groups, divide the total students by the number of students per group.
1025/41 = 25
A library has 1025 books and wants to create stacks of 5 books each. How many stacks will there be?
There will be 205 stacks.
Divide the total number of books by the number of books per stack.
1025/5 = 205
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.