 # Factors of 560: Prime Factorization, Methods, and Examples

The factors of 560 are numbers that, when divided by 560, leave zero as the remainder. The given number’s factors can be positive or negative. ### Factors of 560

Here are the factors of number 560.

Factors of 560: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560.

### Negative Factors of 560

The negative factors of 560 are similar to its positive aspects, just with a negative sign.

Negative Factors of 560 –1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -35, -40, -56, -70, -80, -112, -140, -280, and -560

### Prime Factorization of 560

The prime factorization of 560 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 2 x 5 x 7

In this article, we will learn about the factors of 560 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 560?

The factors of 560 are  1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560. These numbers are the factors as they do not leave any remainder when divided by 560.

The factors of 560 are classified as prime numbers and composite numbers. The prime factors of the number 560 can be determined using the prime factorization technique.

## How To Find the Factors of 560?

You can find the factors of 560 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 560, create a list containing the numbers that are exactly divisible by 560 with zero remainders. One important thing to note is that 1 and 560 are the 560’s factors, as every natural number has one and the number itself as its factor.

One is also called the universal factor of every number. The factors of 560 are determined as follows:

$\dfrac{560}{1} = 560$

$\dfrac{560}{2} = 280$

$\dfrac{560}{3} = 140$

$\dfrac{560}{5} = 112$

$\dfrac{560}{7} = 80$

$\dfrac{560}{8} = 70$

$\dfrac{560}{10} = 56$

$\dfrac{560}{14} = 40$

$\dfrac{560}{16} = 35$

$\dfrac{560}{20} = 28$

Therefore,  1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560 are the factors of 560.

### Total Number of Factors of 560

For 560, there are twenty positive factors and twenty negative ones. So in total, there are 40 factors of 560.

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 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 560 is given as:

Factorization of 560 is 1 x 2$^4$ x 5 x 7.

The exponent of 1, 5, and 7 is 1, whereas the exponent of 2 is 4.

Adding 1 to each and multiplying them together results in 40.

Therefore, the total number of factors of 560 is 40. Twenty are positive, and twenty 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 560 by Prime Factorization

The number 560 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 560 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 560, 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 560 can be expressed as:

560 = 2 x 2 x 2 x 2 x 5 x 7

## Factors of 560 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 560, the factor pairs can be found as:

1 x 560 = 560

2 x 280 = 560

4 x 140 = 560

5 x 112 = 560

7 x 80 = 560

8 x 70 = 560

10 x 56 = 560

14 x 40 = 560

16 x 35 = 560

20 x 28 = 560

The possible factor pairs of 560 are given as (1, 560), (2, 280 ), (4, 140 ), (5, 112 ), (7, 80 ), (8, 70 ), (10, 56 ), (14, 40 ), (16, 35 ) and (20, 28 ).

All these numbers in pairs, when multiplied, give 560 as the product.

The negative factor pairs of 560 are given as:

1 x -560 = 560

-2 x -280 = 560

-4 x -140 = 560

-5 x -112 = 560

-7 x -80 = 560

-8 x -70 = 560

-10 x -56 = 560

-14 x -40 = 560

-16 x -35 = 560

-20 x -28 = 560

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, -7, -8, -10, -14, -16, -20, -28, -35, -40, -56, -70, -80, -112, -140, -280, and -560

are called negative factors of 560.

The list of all the factors of 560, including positive as well as negative numbers, is given below.

Factor list of 560: 1, -1, 2, -2, 4, -4, 5, -5, 7, -7, 8, -8, 10, -10, 14, -14, 16, -16, 20, -20, 28, -28, 35, -35, 40, -40, 56, -56, 70, -70, 80, -80, 112, -112, 140, -140, 280, -280, 560, and -560

## Factors of 560 Solved Examples

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

### Example 1

How many factors of 560 are there?

### Solution

The total number of Factors of 560 is 40.

Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560.

### Example 2

Find the factors of 560 using prime factorization.

### Solution

The prime factorization of 560 is given as:

560 $\div$ 2 = 280

280 $\div$ 2 = 140

140 $\div$ 2 = 70

70 $\div$ 2 = 35

35 $\div$ 5 = 7

7 $\div$ 7 = 7

So the prime factorization of 560 can be written as:

2 x 2 x 2 x 2 x 5 x 7 = 560