 # Factors of 697: Prime Factorization, Methods, and Examples

The factors of 697 are numbers that, when divided by 697, give zero as the remainder. The given number’s factors can be positive and negative. ### Factors of 697

Here are the factors of number 697.

Factors of 697: 1, 17, 41, and 697.

### Negative Factors of 697

The negative factors of 697 are similar to its positive aspects, just with a negative sign.

Negative Factors of 697: –1, -17, -41, and -697

### Prime Factorization of 697

The prime factorization of 697 is the way of expressing its prime factors in the product form. Prime Factorization: 17 x 41

In this article, we will learn about the factors of 697 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 697?

The factors of 697 are 1, 17, 41, and 697. These numbers are the factors as they do not leave any remainder when divided by 697.

The factors of 697 are classified as prime numbers and composite numbers. The prime factors of the number 697 can be determined using the prime factorization technique.

## How To Find the Factors of 697?

You can find the factors of 697 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 697, create a list containing the numbers that are exactly divisible by 697 with zero remainders. One important thing to note is that 1 and 697 are the 697’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 697 are determined as follows:

$\dfrac{697}{1} = 696$

$\dfrac{697}{17} = 41$

Therefore, 1, 17, 41, and 697 are the factors of 697.

### Total Number of Factors of 697

For 697, there are four positive factors and four negative ones. So in total, there are 8 factors of 697.

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 6967 is 1 x 17 x 41.

The exponent of 1, 17, and 41 is 1.

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

Therefore, the total number of factors of 697 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 697 by Prime Factorization

The number 697 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 697 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 697, 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 697 can be expressed as:

697 = 17 x 41

## Factors of 697 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 697, the factor pairs can be found as:

1 x 697 = 679

17 x 41 = 697

The possible factor pairs of 697 are given as (1, 697) and (17, 41).

All these numbers in pairs, when multiplied, give 697 as the product.

The negative factor pairs of 697 are given as:

-1 x -697 = 697

-17 x -41 = 697

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, -17, -41, and -697 are called negative factors of 697.

The list of all the factors of 697, including positive as well as negative numbers, is given below.

Factor list of 697: 1, -1, 17, -17, 41, -41, 697, and -697

## Factors of 697 Solved Examples

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

### Example 1

How many factors of 697 are there?

### Solution

The total number of Factors of 697 is 8.

Factors of 697 are 1, 17, 41, and 697.

### Example 2

Find the factors of 697 using prime factorization.

### Solution

The prime factorization of 697 is given as:

697 $\div$ 17 = 41

41 $\div$ 41 = 1

So the prime factorization of 697 can be written as:

17 x 41 = 697