 # Factors of 698: Prime Factorization, Methods, and Examples

The factors of 698 are numbers that, when divided by 698, leave zero as the remainder. The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers. ### Factors of 698

Here are the factors of number 698.

Factors of 698: 1, 2, 349, and 698.

### Negative Factors of 698

The negative factors of 698 are similar to its positive aspects, just with a negative sign.

Negative Factors of 698: –1, -2, -349, and -698

### Prime Factorization of 698

The prime factorization of 698 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 349

In this article, we will learn about the factors of 698 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 698?

The factors of 698 are 1, 2, 349, and 698. These numbers are the factors as they do not leave any remainder when divided by 698.

The factors of 698 are classified as prime numbers and composite numbers. The prime factors of the number 698 can be determined using the prime factorization technique.

## How To Find the Factors of 698?

You can find the factors of 698 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 698, create a list containing the numbers that are exactly divisible by 698 with zero remainders. One important thing to note is that 1 and 698 are the 698’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 698 are determined as follows:

$\dfrac{698}{1} = 698$

$\dfrac{698}{2} = 349$

Therefore, 1, 2, 349, and 698 are the factors of 698.

### Total Number of Factors of 698

For 698, there are four positive factors and four negative ones. So in total, there are 8 factors of 698.

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 X is given as:

Factorization of 698 is 1 x 3 x 349.

The exponent of 1, 3, and 349 is 1.

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

Therefore, the total number of factors of 698 is 8. Four are positive, and four 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 698 by Prime Factorization

The number 698 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 698 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 698, 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 698 can be expressed as:

698 = 2 x 349

## Factors of 698 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 698, the factor pairs can be found as:

1 x 698 = 698

2 x 349 = 698

The possible factor pairs of 698 are given as (1, 698) and (2, 349).

All these numbers in pairs, when multiplied, give 698 as the product.

The negative factor pairs of 698 are given as:

-1 x -698 = 698

-2 x -349 = 698

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, -349, and -698 are called negative factors of X.

The list of all the factors of 698, including positive as well as negative numbers, is given below.

Factor list of 698: 1, -1, 2, -2, 349, -349, 698, and -698

## Factors of 698 Solved Examples

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

### Example 1

How many factors of 698 are there?

### Solution

The total number of Factors of 698 is 8.

Factors of 698 are 1, 2, 349, and 698.

### Example 2

Find the factors of 698 using prime factorization.

### Solution

The prime factorization of 698 is given as:

698 $\div$ 2 = 349

349 $\div$ 349 = 1

So the prime factorization of 698 can be written as:

2 x 349 = 698