 # Factors of 460: Prime Factorization, Methods, and Examples

Factors of 460 are numbers that, when divided by 460, result in a remainder of zero. Positive and negative factors are acceptable if they are created by multiplying two-factor integers. The number 460 has a total of 12 positive factors.

### Factors of 460

Here are the factors of number 460.

Factors of 460: 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460

### Negative Factors of 460

The negative factors of 460 are similar to its positive aspects, just with a negative sign.

Negative Factors of 460: -1,- 2, -4, -5, -10, -20, -23, -46, -92, -115, -230 and -460

### Prime Factorization of 460

The prime factorization of 460 is the way of expressing its prime factors in the product form.

Prime Factorization: 22 x 5 x 23

In this article, we will learn about the factors of 460 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 460?

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460. These numbers are the factors as they do not leave any remainder when divided by 460.

The factors of 460 are classified as prime numbers and composite numbers. The prime factors of the number 460 can be determined using the prime factorization technique.

## How To Find the Factors of 460?

You can find the factors of 460 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 460, create a list containing the numbers that are exactly divisible by 460 with zero remainders. One important thing to note is that 1 and 460 are the 460’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 460 are determined as follows:

$\dfrac{460}{1} = 460$

$\dfrac{460}{2} = 230$

$\dfrac{460}{4} = 115$

$\dfrac{460}{5} = 92$

$\dfrac{460}{10} = 46$

$\dfrac{460}{20} = 23$

$\dfrac{460}{23} = 20$

$\dfrac{460}{46} = 10$

$\dfrac{460}{92} = 5$

$\dfrac{460}{115} = 4$

$\dfrac{460}{230} = 2$

$\dfrac{460}{460} = 1$

Therefore,  1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460.

### Total Number of Factors of 460

For 460, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 460.

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 460 is given as:

Factorization of 460 is 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460.

The exponent of 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460 is 1.

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

Therefore, the total number of factors 460 is 24. 12 are positive, and 12 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 460 by Prime Factorization

The number 460 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 460 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 460, divide 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 460 can be expressed as:

460 = 22 x 5 x 23

## Factors of 460 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. For 460, the factor pairs can be found as:

1 x 460 = 460

2 x 230= 460

4 x 115 = 460

5 x 92 = 460

10 x 46 = 460

20 x 23 = 460

The possible factor pairs of 460 are given as (1, 460), (2, 230),(4, 115),(5, 92),(10, 46)and (20, 23 ).

All these numbers in pairs, when multiplied, give 460 as the product.

The negative factor pairs of 460 are given as:

-1 x -460 = 460

-a x -b = 460

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, -20, -23, -46, -92, -115, -230 and -460are called negative factors of 460.

The list of all the factors of460, including positive and negative numbers, is given below.

Factor list of 460: 1,-1,2,-2, 4,-4,5, -5,10, -10, 20,-20, 23,-23,46, -46,92, -92,115, -115, 230,-230, 460 and -460

## Factors of 460 Solved Examples

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

### Example 1

How many factors of 460 are there?

### Solution

The total number of Factors 460 is 24.

Factors of 460 are1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460.

### Example 2

Find the factors of 460 using prime factorization.

### Solution

The prime factorization of 460 is given as:

460 $\div$ 2 =230

230 $\div$ 2 = 115

115 $\div$ 5 =23

23 $\div$ 23 = 1

So the prime factorization of 460 can be written as:

22 x 5 x 23 = 460