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Factors of 260: Prime Factorization, Methods, and Examples

The factors of 260 are natural numbers that give the number 260 when multiplied together.  The number 260 has more than two factors; such a number is known as composite. In other words, the factors perfectly divide the given number.

To determine the factor, the prime factorization method is used.

Factors of 260

Here are the factors of number 260.

Factors of 260: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

Negative Factors of 260

The negative factors of 260 are similar to its positive factors, just with a negative sign.

Negative Factors of 260: -1, -2, -4, -5, -10, -13, -20, -26, -52, -65, -130, and -260

Prime Factorization of 260

The prime factorization of 260 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 5 x 13

In this article, we will learn about the factors of 260 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 260?

The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260. All of these numbers are the factors as they do not leave any remainder when divided by 260.

The factors of 260 are classified as prime numbers and composite numbers. The prime factors of the number 260 can be determined using the technique of prime factorization.

How To Find the Factors of 260?

You can find the factors of 260 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 260, create a list containing the numbers that are exactly divisible by 260 with zero remainders. One important thing to note is that 1 and 260 are the 260’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 260 are determined as follows:

\[\dfrac{260}{1} = 260\]

\[\dfrac{260}{2} = 130\]

\[\dfrac{260}{4} = 65\]

\[\dfrac{260}{5} = 52\]

\[\dfrac{260}{10} = 26\]

\[\dfrac{260}{260} = 1\]

Therefore, 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260 are the factors of 260.

Total Number of Factors of 260

For 260, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 260. 

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

  1. Find the 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 260 is given as:

Factorization of 260 is 1 x $2^{2}$ x 5 x 13.

The exponent of 1, 5, and 13 is 1, whereas the exponent of 2 is 2.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 260 is 24. Twelve are positive, and 12 factors are negative.

Important Notes

Here are some important 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 260 by Prime Factorization

The number 260 is 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.

Before finding the factors of 260 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 260, start dividing by its smallest 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 260 can be expressed as:

260 = $2^{2}$ x 5 x 13

Factors of 260 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 of the given numbers.

For 260, the factor pairs can be found as:

1 x 260 = 260

2 x 130 = 260 

4 x 65 = 260 

5 x 52 = 260 

10 x 26 = 260 

13 x 20 = 260 

The possible factor pairs of 260 are given as (1, 260), (2, 130), (4, 65), (5, 52), (10, 26), and (13, 20).

All these numbers in pairs, when multiplied, give 260 as the product.

The negative factor pairs of 260 are given as:

-1 x -260 = 260

-2 x -130 = 260 

-4 x -65 = 260 

-5 x -52 = 260 

-10 x -26 = 260 

-13 x -20 = 260

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, -2, -4, -5, -10, -13, -20, -26, -52, -65, -130 and -260 are called negative factors of 260.

The list of all the factors of 260, including positive as well as negative numbers, is given below.

Factor list of 260: 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 13, -13, 20, -20, 26, -26, 52, -52, 65, -65, 130, -130, 260, and -260

Factors of 260 Solved Examples

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

Example 1

How many factors of 260 are there?

Solution

The total number of Factors of 260 is 12.

Factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130 and 260.

Example 2

Find the factors of 260 using prime factorization.

Solution

The prime factorization of 260 is given as:

260 $\div$ 2 = 130 

130 $\div$ 2 = 65 

65 $\div$ 5 = 13 

13 $\div$ 13 = 1 

So the prime factorization of 260 can be written as:

$2^{2}$ x 5 x 13 = 260

Factors of 259|Factors List| Factors of 261

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