Factors of 1325
2026-02-28 09:14 Diff
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Last updated on December 12, 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 1325, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1325?

The numbers that divide 1325 evenly are known as factors of 1325.

A factor of 1325 is a number that divides the number without a remainder.

The factors of 1325 are 1, 5, 13, 25, 53, 65, 265, and 1325.

Negative factors of 1325: -1, -5, -13, -25, -53, -65, -265, and -1325.

Prime factors of 1325: 5 and 53.

Prime factorization of 1325: 5 × 53.

The sum of factors of 1325: 1 + 5 + 13 + 25 + 53 + 65 + 265 + 1325 = 1752

How to Find Factors of 1325?

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 1325. Identifying the numbers that are multiplied to get the number 1325 is the multiplication method.

Step 1: Multiply 1325 by 1, 1325 × 1 = 1325.

Step 2: Check for other numbers that give 1325 after multiplying:

5 × 265 = 1325

13 × 102 = 1325

25 × 53 = 1325

Therefore, the positive factor pairs of 1325 are: (1, 1325), (5, 265), (13, 102), (25, 53).

For every positive factor, there is a negative factor.

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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 as a whole number as factors. Factors can be calculated by following a simple division method

Step 1: Divide 1325 by 1, 1325 ÷ 1 = 1325.

Step 2: Continue dividing 1325 by the numbers until the remainder becomes 0.

1325 ÷ 1 = 1325

1325 ÷ 5 = 265

1325 ÷ 13 = 102

1325 ÷ 25 = 53

Therefore, the factors of 1325 are: 1, 5, 13, 25, 53, 65, 265, 1325.

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: In this process, prime factors of 1325 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1325 ÷ 5 = 265

265 ÷ 5 = 53

53 ÷ 53 = 1

The prime factors of 1325 are 5 and 53.

The prime factorization of 1325 is: 5 × 53.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 1325 is divided by 5 to get 265.

Step 2: Now divide 265 by 5 to get 53.

Step 3: Here, 53 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1325 is: 5 × 53.

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 1325: (1, 1325), (5, 265), (13, 102), (25, 53).

Negative factor pairs of 1325: (-1, -1325), (-5, -265), (-13, -102), (-25, -53).

Common Mistakes and How to Avoid Them in Factors of 1325

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 5 teams and 1325 apples. How will they divide it equally?

Okay, lets begin

They will get 265 apples each.

Explanation

To divide the apples equally, we need to divide the total apples with the number of teams.

1325/5 = 265

Well explained 👍

Problem 2

A rectangular garden has a length of 25 meters and a total area of 1325 square meters. Find the width.

Okay, lets begin

53 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

1325 = 25 × width

To find the value of width, we need to shift 25 to the left side.

1325/25 = width

Width = 53.

Well explained 👍

Problem 3

There are 13 boxes and 1325 marbles. How many marbles will be in each box?

Okay, lets begin

Each box will have 102 marbles.

Explanation

To find the marbles in each box, divide the total marbles with the boxes.

1325/13 = 102

Well explained 👍

Problem 4

In a class, there are 1325 students, and 5 groups. How many students are there in each group?

Okay, lets begin

There are 265 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

1325/5 = 265

Well explained 👍

Problem 5

1325 books need to be arranged in 53 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 25 books.

Explanation

Divide total books with shelves.

1325/53 = 25

Well explained 👍

FAQs on Factors of 1325

1.What are the factors of 1325?

1, 5, 13, 25, 53, 65, 265, 1325 are the factors of 1325.

2.Mention the prime factors of 1325.

The prime factors of 1325 are 5 × 53.

3.Is 1325 a multiple of 25?

4.Mention the factor pairs of 1325?

(1, 1325), (5, 265), (13, 102), (25, 53) are the factor pairs of 1325.

5.What is the square of 1325?

The square of 1325 is 1,755,625.

Important Glossaries for Factors of 1325

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1325 are 1, 5, 13, 25, 53, 65, 265, and 1325.
     
  • Prime factors: The factors which are prime numbers. For example, 5 and 53 are prime factors of 1325.
     
  • 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 1325 are (1, 1325), (5, 265), etc.
     
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1325 is 5 × 53.
     
  • Negative factors: Factors that are negative integers. For example, -1, -5, -13, -25, etc., are negative factors of 1325.

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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.