# Factors of 723: Prime Factorization, Methods, and Examples

723 is an odd composite number that has 4 factors in total. 1, the universal factor, is its smallest factor whereas, 723 itself is the largest. Its smallest prime factor is 3 which is also the smallest odd prime number to exist on the number line.

Other then the smallest and the largest factor all other factors are prime numbers.

### Factors of 723

Here are the factors of number 723.

Factors of 723: 1, 3, 241, and 723

### Negative Factors of 723

The negative factors of 723 are similar to its positive aspects, just with a negative sign.

Negative Factors of 723: -1, -3, -241, and -723

### Prime Factorization of 723

The prime factorization of 723 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 241

In this article, we will learn about the factors of 723 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 723?

The factors of 723 are 1, 3, 241, and 723. These numbers are the factors as they do not leave any remainder when divided by 723.

The factors of 723 are classified as prime numbers and composite numbers. The prime factors of the number 723 can be determined using the prime factorization technique.

## How To Find the Factors of 723?

You can find the factors of 723 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 723, create a list containing the numbers that are exactly divisible by 723 with zero remainders. One important thing to note is that 1 and 723 are the 723’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 723 are determined as follows:

$\dfrac{723}{1} = 723$

$\dfrac{723}{3} = 241$

$\dfrac{723}{241} = 3$

$\dfrac{723}{723} = 1$

Therefore, 1, 3, 241, and 723 are the factors of 723.

### Total Number of Factors of 723

For 723, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 723.

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 723 is given as:

Factorization of 723 is 1 x 3 x 241.

The exponent of 1, 3, and 241 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 723 is 8. 4 are positive, and 4 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 723 by Prime Factorization

The number 723 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 723 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 723, 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 723 can be expressed as:

723 = 3 x 241

## Factors of 723 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 X, the factor pairs can be found as:

1 x 723 = 723

3 x 241 = 723

The possible factor pairs of 723 are given as (1, 723) and (3,241 ).

All these numbers in pairs, when multiplied, give 723 as the product.

The negative factor pairs of 723 are given as:

-1 x -723 = 723

-3 x -241 = 723

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, -3, -241, and -723 are called negative factors of X.

The list of all the factors of 723, including positive as well as negative numbers, is given below.

Factor list of 723: 1, -1, 3, -3, 241, -241, 723, and -723

## Factors of 723 Solved Examples

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

### Example 1

How many factors of 723 are there?

### Solution

The total number of Factors of 723 is 4.

Factors of 723 are1, 3, 241, 723.

### Example 2

Find the factors of 723 using prime factorization.

### Solution

The prime factorization of 723 is given as:

723 $\div$ 3 = 241

241 $\div$ 241 = 1

So the prime factorization of 723 can be written as:

3 x 241 = 723