# Factors of 704: Prime Factorization, Methods, and Examples

There are fourteen positive factors of the number 704 which when divided by 704 give us the number which is decimal without decimal places.

If the quotient is not a whole number then the number used as a divisor is not the factor of 704.

### Factors of 704

Here are the factors of number 704.

Factors of 704: 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, and 704

### Negative Factors of 704

The negative factors of 704 are similar to its positive aspects, just with a negative sign.

Negative Factors of 704: -1, -2, -4, -8, -11, -16, -22, -32, -44, -64, -88, -176, -352, and -704

### Prime Factorization of 704

The prime factorization of 704 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 2 x 2 x 2 x 11

In this article, we will learn about the factors of 704 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 704?

The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, and 704. These numbers are the factors as they do not leave any remainder when divided by 704.

The factors of 704 are classified as prime numbers and composite numbers. The prime factors of the number 704 can be determined using the prime factorization technique.

## How To Find the Factors of 704?

You can find the factors of 704 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 704, create a list containing the numbers that are exactly divisible by 704 with zero remainders. One important thing to note is that 1 and 704 are the 704’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 704 are determined as follows:

$\dfrac{704}{1} = 704$

$\dfrac{704}{2} = 352$

$\dfrac{704}{4} = 176$

$\dfrac{704}{8} = 88$

$\dfrac{704}{11} = 64$

$\dfrac{704}{16} = 44$

$\dfrac{704}{22} = 32$

$\dfrac{704}{32} = 22$

$\dfrac{704}{704} = 1$

Therefore, 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, and 704 are the factors of 704.

### Total Number of Factors of 704

For 704, there are 14 positive factors and 14 negative ones. So in total, there are 28 factors of 704.

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 704 is given as:

Factorization of 704 is 2 x 2 x 2 x 2 x 2 x 2 x 11.

The exponent of 2 and 11 is 6, 1.

Adding 1 to each and multiplying them together results in 14.

Therefore, the total number of factors of 704 is 28. Fourteen are positive, and fourteen 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 704 by Prime Factorization

The number 704 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 704 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 704, 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 704 can be expressed as:

704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

## Factors of 704 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 704, the factor pairs can be found as:

1 x 704 = 704

2 x 352 = 704

4 x 176 = 704

8 x 88 = 704

11 x 64 = 704

16 x 44 = 704

22 x 32 = 704

The possible factor pairs of 704 are given as (1, 704), (2, 352), (4, 176), (8, 88), (11, 64), (16, 44), and (22, 32).

All these numbers in pairs, when multiplied, give 704 as the product.

The negative factor pairs of 704 are given as:

-1 x -704 = 704

-2 x -352 = 704

-4 x -176 = 704

-8 x -88 = 704

-11 x -64 = 704

-16 x -44 = 704

-22 x -32 = 704

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, -8, -11, -16, -22, -32, -44, -64, -88, -176, -352, and -704 are called negative factors of 704.

The list of all the factors of 704, including positive as well as negative numbers, is given below.

Factor list of 704: 1, -1, 2, -2, 4, -4, 8, -8, 11, -11, 16, -16, 22, -22,32, -32, 44, -44, 64, -64, 88, -88, 176, -176, 352, -352, 704, and -704

## Factors of 704 Solved Examples

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

### Example 1

How many factors of 704 are there?

### Solution

The total number of Factors of 704 is 14.

Factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352,  and 704

.

### Example 2

Find the factors of 704 using prime factorization.

### Solution

The prime factorization of 704 is given as:

704 $\div$ 2 = 352

352 $\div$ 2 = 176

176 $\div$ 2 = 88

88 $\div$ 2 = 44

44 $\div$ 2 = 22

22 $\div$ 2 = 11

11 $\div$ 11 = 1

So the prime factorization of 704 can be written as:

2 x 2 x 2 x 2 x 2 x 2 x 11 = 704