# Factors of 722: Prime Factorization, Methods, and Examples

722 has a total of 6 factors. These are the numbers that completely divide 722. Â The factors of a number are always integers or whole numbers.Â

When 722 is divided by any of its factors the quotient is also an integer and the quotient and the divisor are called the factor pairs.

### Factors of 722

Here are the factors of number 722.

Factors of 722: 1, 2, 19, 38, 361, and 722.

### Negative Factors of 722

The negative factors of 733Â are similar to its positive aspects, just with a negative sign.

Negative Factors of 722: -1, -2, -19, -38, -361, and -722.

### Prime Factorization of 722

The prime factorization of 722Â is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 19$^2$

In this article, we will learn about the factors of 722 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 722?

The factors of 722 are 1, 2, 19, 38, 361, and 722.. These numbers are the factors as they do not leave any remainder when divided by 722.

The factors of 722 are classified as prime numbers and composite numbers. The prime factors of the number 722 can be determined using the prime factorization technique.

## How To Find the Factors of 722?

You can find the factors of 722Â 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 X, create a list containing the numbers that are exactly divisible by X with zero remainders. One important thing to note is that 1 and 722 are the 722’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 722 are determined as follows:

$\dfrac{722}{1} = 722$

$\dfrac{722}{2} = 361$

$\dfrac{722}{19} = 38$

$\dfrac{722}{38} = 19$

$\dfrac{722}{361} = 2$

$\dfrac{722}{722} = 1$

Therefore, 1, 2, 19, 38, 361, and 722. are the factors of 722.

### Total Number of Factors of 722

For 722, there are 6Â positive factors and 6Â negative ones. So in total, there are 12 factors of 722.Â

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 722 is given as:

Factorization of 722 is 1 x 2 x 19$^2$.

The exponent of 1 and 2 is 1 whereas the exponent of 19 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of X722is 12. 6 are positive, and 6 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 722 by Prime Factorization

The number 722 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 722 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 722, 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 722Â can be expressed as:

722 = 2 x 19 $^2$Â

## Factors of 722 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 722, the factor pairs can be found as:

1 x 722 = 722

2 x 361 = 722Â

19 x 38 = 722Â

The possible factor pairs of 722 are given asÂ (1, 722), (2, 361), and (19, 38).

All these numbers in pairs, when multiplied, give 722 as the product.

The negative factor pairs of 722 are given as:

-1 x -722 = 722Â

-2 x -361 = 722

-19 x -38 – 722

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, -19, -38, -361, and 722. are called negative factors of 722.

The list of all the factors of 722, including positive as well as negative numbers, is given below.

Factor list of 722: 1, -1, 2, -2, 19, -19, 361, -361, 722, and -722

## Factors of 722 Solved Examples

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

### Example 1

How many factors of 722 are there?

### Solution

The total number of Factors of 722 is 6.

Factors of 722 are 1, 2, 19, 38, 361, and 722.

### Example 2

Find the factors of 722 using prime factorization.

### Solution

The prime factorization of 722 is given as:

722 $\div$ 2 = 361Â

722 $\div$ 2 = 19Â

v19 $\div$ 19 = 1Â

So the prime factorization of 722 can be written as:

2 x 19$^2$ = 722