 # Factors of 475: Prime Factorization, Methods, and Examples

The factors of 475  are the group of numbers that can be easily divided by 475 without any remainders. The number 475 is an odd composite with six factors in total. The factors of 475 can be positive and negative.

### Factors of 475

Here are the factors of number 475.

Factors of 475: 1, 5, 19, 25, 95, and 475

### Negative Factors of 475

The negative factors of 475 are similar to their positive aspects, just with a negative sign.

Negative Factors of 475: –1, -5, -19, -25, -95, and -475

### Prime Factorization of 475

The prime factorization of 475 is the way of expressing its prime factors in the product form.

Prime Factorization: 5 x 5 x 19

In this article, we will learn about the factors of 475 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 475?

The factors 475 are 1, 5, 19, 25, 95, and 475. These numbers are the factors as they do not leave any remainder when divided by 475.

The factors of 475 are classified as prime numbers and composite numbers. The prime factors of the number 475 can be determined using the prime factorization technique.

## How To Find the Factors of 475?

You can find the factors of 475 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 475, create a list containing the numbers precisely divisible by 475 with zero remainders. One important thing to note is that 1 and 475 are 475’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 475 are determined as follows:

$\dfrac{475}{1} = 475$

$\dfrac{475}{5} = 95$

$\dfrac{475}{19} = 25$

Therefore, 1, 5, 19, 25, 95, and 475 are the factors of 475.

### Total Number of Factors of 475

For 475, there are six positive factors and six negative ones. So in total, there are twelve factors of 475.

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 twelve is given as:

Factorization of 475 is 1 x 5$^2$ x 19.

The exponent of 1 and 19 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 475 is 12. Six 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 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 475 by Prime Factorization

The number 475 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. Before finding the factors of 475 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 475, 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 475 can be expressed as:

475 = 5 x 5 x 19

## Factors of 475 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 475, the factor pairs can be found as:

1 x 475 = 475

5 x 95 = 475

19 x 25 = 475

The possible factor pairs of 475 are given as (1, 475), (5, 95), and (19, 25).

All these numbers in pairs, when multiplied, give 475 as the product.

The negative factor pairs of 475 are given as:

1 x -475 = 475

-5 x -95 = 475

-19 x -25 = 475

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, -19, -25, -95, and -475 are called negative factors of 475.

The list of all the factors of 475, including positive and negative numbers, is given below.

Factor list of 475: 1, -1, 5, -5, 19, -19, 25, -25, 95, -95, 475, and -475

## Factors of 475 Solved Examples

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

### Example 1

How many factors of 475 are there?

### Solution

The total number of Factors of 475 is six.

Factors of 475 are 1, 5, 19, 25, 95, and 475.

### Example 2

Find the factors of 475 using prime factorization.

### Solution

The prime factorization of 475 is given as:

475 $\div$ 5 = 95

95 $\div$ 5 = 17

17 $\div$ 17 = 1

So the prime factorization of 475 can be written as:

5 x 5 x 17 = 475