Factors of 325
2026-02-28 08:36 Diff
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Last updated on December 11, 2025

Factors of 325 are numbers that divide 325 completely without leaving a remainder. These factors are useful in various real-life applications, such as organizing and distributing resources evenly. In this article, we will explore the factors of 325 and the different methods to find them.

What are the Factors of 325?

The factors of 325 are the numbers that divide 325 evenly.

The factors of 325 are 1, 5, 13, 25, 65, and 325.


Negative Factors: Negative factors are the counterparts of the positive factors but in a negative form. They also divide 325 completely without leaving a remainder.


Negative Factors: -1, -5, -13, -25, -65, -325


Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 325 as the product.


Prime Factors: 5, 13


Prime Factorization: Prime factorization involves expressing 325 as a product of its prime factors. For 325, the prime factorization is:


Prime Factorization: 51 × 51 × 131

Table listing the factors of 325:

Positive Factors

1, 5, 13, 25, 65, 325

Negative Factors

-1, -5, -13, -25, -65, -325

Prime Factors

5, 13

Prime Factorization

51 × 51 × 131

This breakdown helps in understanding the various factors of 325, whether they are positive or negative, as well as how prime factorization works for this number.

How to Find the Factors of 325?

There are different methods to find the factors of 325. Below are some of the common methods:

Methods to Find the Factors of 325:

  1. Multiplication Method
  2. Division Method
  3. Prime Factorization
  4. Factor Tree

Finding Factors Using the Multiplication Method

The multiplication method helps find pairs of numbers that, when multiplied together, result in 325.


Step 1: Find pairs of numbers whose product is 325.


Step 2: The factors are the numbers that, when multiplied, give 325.


Step 3: List the pairs of numbers whose product equals 325.


The list of numbers whose products are 325 is given below:
1 × 325 = 325
5 × 65 = 325
13 × 25 = 325

Thus, the factors of 325 are 1, 5, 13, 25, 65, and 325.

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Finding Factors Using the Division Method

The division method finds the numbers that divide 325 completely. The steps are as follows:


Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 325 ÷ 1 = 325


Step 2: Move to the next integers and divide 325 by them. Both the divisor and quotient are factors of 325.

  • 325 ÷ 5 = 65
  • 325 ÷ 13 = 25

Thus, the factors of 325 are 1, 5, 13, 25, 65, and 325.

Prime Factors and Prime Factorization

Prime factors are prime numbers that, when multiplied together, give the given number. Prime factorization breaks down a number into its prime factors.


Prime Factors of 325:


The prime factors of 325 are 5 and 13. To find the prime factors, we divide 325 by these prime numbers.


Step 1: Divide 325 by the prime number 5

  • 325 ÷ 5 = 65


Step 2: Divide 65 by the prime number 13

  • 65 ÷ 13 = 5


Step 3: Divide 5 by the prime number 5

  • 5 ÷ 5 = 1


Prime Factorization of 325:


The prime factorization of 325 is the product of its prime factors.


Prime Factorization of 325: 51 × 51 × 131

Factor Tree

A factor tree visually represents the prime factorization of a number. Each branch of the tree splits into prime factors, helping to understand the process clearly.
  

This tree shows the breakdown of 325 into its prime factors: 5 × 5 × 13.

Positive and Negative Factor Pairs of 325:


Factors of 325 can be written in both positive and negative pairs. These pairs multiply to give the number 325.


Positive Factor Pairs: (1, 325), (5, 65), (13, 25)
Negative Factor Pairs: (-1, -325), (-5, -65), (-13, -25)


By using these methods, you can easily find the factors of 325, whether positive or negative and understand its prime factorization.
 

Common Mistakes and How to Avoid Them in Factors of 325

Mistakes can happen when finding the factors of 325. Below are some common errors and tips on how to avoid them for accurate factor identification.

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Problem 1

If 325 is divided by 5, how much does each share get?

Okay, lets begin

325÷5=65

Explanation

When 325 is divided by 5, the quotient is 65. Hence, each share gets 65.

Well explained 👍

Problem 2

Determine the square root of 325.

Okay, lets begin

The square root of 325 is approximately 18.03.

Explanation

18.03×18.03=325. This shows that 18.03 is the approximate square root.

Well explained 👍

Problem 3

Can 325 be divided evenly by 13?

Okay, lets begin

To check divisibility, divide 325÷13. The result is 25, which is an integer.

Explanation

Since 325 divided by 13 gives a whole number (25), 325 is divisible by 13.

Well explained 👍

Problem 4

What is the greatest common divisor (GCD) of 325 and 65?

Okay, lets begin

The GCD of 325 and 65 is 65.

Explanation

  • The factors of 325 are 1,5,13,25,65,1, 5, 13, 25, 65,1,5,13,25,65, and 325325325.
  • The factors of 65 are 1,5,13,1, 5, 13,1,5,13, and 656565.
  • The common factors are 1,5,13,1, 5, 13,1,5,13, and 656565.

The greatest among these is 656565. Hence, the GCD is 65.

Well explained 👍

FAQs on Factors of 325

1.What are the factors of 325?

The factors of 325 are: 1, 5, 13, 25, 65, and 325.

2.How do you determine if a number is a factor of 325?

A number is a factor of 325 if dividing 325 by that number results in a whole number (without a remainder).

3.What is the smallest factor of 325?

The smallest factor of 325 is 1.

4.What is the largest factor of 325?

The largest factor of 325 is 325 itself.

5.How many factors does 325 have?

325 has 6 factors: 1, 5, 13, 25, 65, and 325.

6.How many odd factors does 325 have?

325 has 6 odd factors: 1, 5, 13, 25, 65, and 325.

7.What factors go into 325?

The factors of 325 are numbers that divide 325 without leaving a remainder, including 1, 5, 13, 25, 65, and 325.

8.How many factors of 325 are perfect squares?

Important glossaries for the Factors of 325

  • Co-prime: Numbers having 1 as the only common factor.
     
  • Perfect Square: The number we get when the same number is multiplied twice.
     
  • Prime Factors: Prime numbers, which are factors of a given number
     
  • Factor Tree: A tree diagram used to represent the prime factors of a given number.
     
  • Multiple: Numbers we get when another number multiplies the given number.

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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.