# Factors of 728: Prime Factorization, Methods, and Examples

Evenly divisible factors of 728 are sixteen positive number and sixteen negative ones.

When these factors place in the denominator and 728 in numerator give whole number in result.

### Factors of 728

Here are the factors of number 728.

Factors of 728: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728

### Negative Factors of 728

The negative factors of 728 are similar to its positive aspects, just with a negative sign.

Negative Factors of 728: -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, and -728

### Prime Factorization of 728

The prime factorization of 728 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 7 x 13

In this article, we will learn about the factors of 728 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 728?

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728. These numbers are the factors as they do not leave any remainder when divided by 728.

The factors of 728 are classified as prime numbers and composite numbers. The prime factors of the number 728 can be determined using the prime factorization technique.

## How To Find the Factors of 728?

You can find the factors of 728 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 728, create a list containing the numbers that are exactly divisible by 728 with zero remainders. One important thing to note is that 1 and 728 are the 728’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 728 are determined as follows:

$\dfrac{728}{1} = 728$

$\dfrac{728}{2} = 364$

$\dfrac{728}{4} = 182$

$\dfrac{728}{7} = 104$

$\dfrac{728}{8} = 91$

$\dfrac{728}{13} = 56$

$\dfrac{728}{14} = 52$

$\dfrac{728}{26} = 28$

$\dfrac{728}{728} = 1$

Therefore, 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 are the factors of 728.

### Total Number of Factors of 728

For 728, there are sixteen positive factors and sixteen negative ones. So in total, there are 32 factors of 728.

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 728 is given as:

Factorization of 728 is 2 x 2 x 2 x 7 x 13.

The exponent of 2, 7, and 13 is 1,3,1.

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

Therefore, the total number of factors of 728 is 32 whereas sixteen are positive, and sixteen 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 728 by Prime Factorization

The number 728 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 728 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 728, 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 728 can be expressed as:

728 = 2 x 2 x 2 x 7 x 13

## Factors of 728 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 728, the factor pairs can be found as:

1 x 728 = 728

2 x 364 = 728

4 x 182 = 728

7 x 104 = 728

8 x 91 = 728

13 x 56 = 728

14 x 52 = 728

26 x 28 = 728

The possible factor pairs of 728 are given as (1, 728), (2, 364), (4, 182), (7, 104), (8, 91), (13, 56),(14, 52)and (26, 28).

All these numbers in pairs, when multiplied, give 728 as the product.

The negative factor pairs of 728 are given as:

-1 x -728 = 728

-2 x -364 = 728

-4 x -182 = 728

-7 x -104 = 728

-8 x -91 = 728

-13 x -56 = 728

-14 x -52 = 728

-26 x -28 = 728

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, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, and -728 are called negative factors of 728.

The list of all the factors of 728, including positive as well as negative numbers, is given below.

Factor list of 728: 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 13, -13, 14, -14, 26, -26, 28, -28, 52, -52, 56, -56, 91, -91, 104, -104, 182, -182, 364, -364, 728, and -728

## Factors of 728 Solved Examples

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

### Example 1

How many factors of 728 are there?

### Solution

The total number of Factors of 728 is 16.

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

### Example 2

Find the factors of 728 using prime factorization.

### Solution

The prime factorization of 728 is given as:

728 $\div$ 2 = 364

364 $\div$ 2 = 182

182 $\div$ 2 = 91

91 $\div$ 7 = 13

13 $\div$ 13 = 1

So the prime factorization of 728 can be written as:

2 x 2 x 2 x 7 x 13 = 728