JUMP TO TOPIC

# Factors of 561: Prime Factorization, Methods, and Examples

The **factors of 561** are the group of natural numbers that divide number 561 into equal parts. The number 561 is an odd composite which indicates that it has more than two factors.

Let us learn about the concept in detail.

### Factors of 561

Here are the factors of number** 561.**

**Factors of 561**: 1, 3, 11, 17, 33, 51, 187, and 561.

### Negative Factors of 561

The **negative factors of 561** are similar to their positive aspects, just with a negative sign.

**Negative Factors of 561**: –1, -3, -11, -17, -33, -51, -187, and -561

### Prime Factorization of 561

The **prime factorization of 561** is the way of expressing its prime factors in the product form.

**Prime Factorization**: 3 x 11 x 17

In this article, we will learn about the **factors of 561 **and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 561?

**The factors of 561 are ****1, 3, 11, 17, 33, 51, 187, and 561****. These numbers are the factors as they do not leave any remainder when divided by 561.**

The **factors of 561** are classified as prime numbers and composite numbers. The prime factors of the number 561 can be determined using the prime factorization technique.

## How To Find the Factors of 561?

You can find the **factors of 561** 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 561, create a list containing the numbers exactly divisible by 561 with zero remainders. One important thing to note is that 1 and 561 are the 561’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 561 are determined as follows:

\[\dfrac{561}{1} = 561\]

\[\dfrac{561}{3} = 187\]

\[\dfrac{561}{11} = 51\]

\[\dfrac{561}{17} = 33\]

Therefore, 1, 3, 11, 17, 33, 51, 187, and 561 are the factors of 561.

### Total Number of Factors of 561

For 561, there are eight** positive factors** and eight** negative** ones. So in total, there are 16 factors of 561.

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

- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- 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 561 is given as:

Factorization of 561 is** 1 x 3 x 11 x 17**.

The exponent of 1, 3, 11, and 17 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the **total number of factors** of 561 is 6. Eight are positive, and eight 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 number factors 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 561 by Prime Factorization

The **number 561** is a composite number. 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 561 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 561, 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 561** can be expressed as:

**561 = 3 x 11 x 17**

## Factors of 561 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.

For 561, the factor pairs can be found as:

**1 x 561 = 561**

**3 x 187 = 561**

**11 x 51 = 561**

**17 x 33 = 561**** **

1, 3, 11, 17, 33, 51, 187, and 561

The possible** factor pairs of 561 **are given as **(1, 561),** **(3, 187 ),** **(11, 51 )**** **and **(17, 33)**.

All these numbers in pairs, when multiplied, give 561 as the product.

The **negative factor pairs** of 561 are given as:

**-1 x -561 = 561**

**-3 x -187 = 561**

**-11 x -51 = 561**

**-17 x -33 = 561**** **

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, -3, -11, -17, -33, -51, -187, and -561 are called negative factors of 561.

The list of all the factors of 561, including positive as well as negative numbers, is given below.

**Factor list of 561: 1, -1, 3, -3, 11, -11, 17, -17, 33, -33, 51, -51, 187, -187, 561, and -561**

## Factors of 561 Solved Examples

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

### Example 1

How many factors of 561 are there?

### Solution

The total number of Factors of 561 is 16.

Factors of 561 are 1, 3, 11, 17, 33, 51, 187, and 561.

### Example 2

Find the factors of 561 using prime factorization.

### Solution

The prime factorization of 561 is given as:

**561 $\div$ 3 = 187 **

**187 $\div$ 11 = 17 **

**17 $\div$ 17 = 1 **

So the prime factorization of 561 can be written as:

**3 x 11 x 17 = 561**