Factors of 325: Prime Factorization, Methods, and Examples

The factors of 325 are the numbers that can divide by 325. The number 325 is an odd composite with six factors in total. 

Factors Of 325

In this lesson, we will dive deeper and dig more information about the factors of 325.

Factors of 325

Here are the factors of number 325.

Factors of 325: 1, 5, 13, 25, 65, and 325 

Negative Factors of 325

The negative factors of 325 are similar to its positive aspects, just with a negative sign.

Negative Factors of 325: –1, -5, -13, -25, -65, and -325

Prime Factorization of 325

The prime factorization of 325 is the way of expressing its prime factors in the product form.

Prime Factorization: 5 x 5 x 13

In this article, we will learn about the factors of 325 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 325?

The factors of 325 are 1, 5, 13, 25, 65, and 325. These numbers are the factors as they do not leave any remainder when divided by 325.

The factors of 325 are classified as prime numbers and composite numbers. The prime factors of the number 325 can be determined using the prime factorization technique.

How To Find the Factors of 325?

You can find the factors of 325 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 325, create a list containing the numbers that are exactly divisible by 325 with zero remainders. One important thing to note is that 1 and 325 are the 325’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of X are determined as follows:

\[\dfrac{325}{1} = 325\]

\[\dfrac{325}{5} = 65\]

\[\dfrac{325}{13} = 25\]

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

Total Number of Factors of 325

For 325, there are six positive factors and six negative ones. So in total, there are twelve factors of 325. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of 325 is 1 x 5$^2$ x 13.

The exponent of 1 and 13 is 1. The exponent of 5 is 2. 

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 325 is twelve. Six factors are positive, and six factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 325 by Prime Factorization

The number 325 is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.prime factorization of 325

Before finding the factors of 325 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 325, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 325 can be expressed as:

325 = 5$^2$ x 13

Factors of 325 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.Factors of 325 in Pairs

For 325, the factor pairs can be found as:

1 x 325 = 325

5 x 65 = 325 

13 x 25 = 325 

The possible factor pairs of 325 are given as (1, 325), (5, 65), and (13, 25).

All these numbers in pairs, when multiplied, give 325 as the product.

The negative factor pairs of 325 are given as:

-1 x -325 = 325

-5 x -65 = 325 

-13 x -25 = 325 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, –1, -5, -13, -25, -65, and -325 are called negative factors of 325.

The list of all the factors of 325, including positive as well as negative numbers, is given below.

Factor list of 325: 1, -1, 5, -5, 13, -13, 25, -25, 65, -65, 325, and -325

Factors of 325 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 325 are there?


The total number of Factors of 325 is six.

Factors of 325 are1, 5, 13, 25, 65, and 325. 

Example 2

Find the factors of 325 using prime factorization.


The prime factorization of 325 is given as:

325 $\div$ 5 = 65

65 $\div$ 5 = 13  

13 $\div$ 13 = 1 

So the prime factorization of 325 can be written as:

5 x 5 x 13 = 325

Factors of 324|Factors List| Factors of 326