Factors of 691: Prime Factorization, Methods, and Examples

The variables of 691 are those numbers that take off zero as the leftover portion when duplicated by 691. These components completely isolated  691. There are two components within the prime number  691. 

Factors Of 691

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Factors of 691

Here are the factors of number 691.

Factors of 691: 1, and 691

Negative Factors of 691

The negative factors of 691 are similar to their positive aspects, just with a negative sign.

Negative Factors of 691: -1,  and -691

Prime Factorization of 691

The prime factorization of 691 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 691

In this article, we will learn about the factors of 691 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 691?

The factors of 691 are 1,  and 691. These numbers are the factors as they do not leave any remainder when divided by 691.

The factors of 691 are classified as prime numbers and composite numbers. The prime factors of the number 691 can be determined using the prime factorization technique.

How To Find the Factors of 691?

You can find the factors of 691 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 691, create a list containing the numbers that are exactly divisible by691 with zero remainders. One important thing to note is that 1 and 691 are 691’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 691 are determined as follows:

\[\dfrac{691}{1} = 691\]

\[\dfrac{691}{691} = 1\]

Therefore, 1, and 691 are the factors of 691.

Total Number of Factors of 691

For 691, there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 691. 

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 691 is given as:

Factorization of 691 is 1 x 691.

The exponent of 1 is 1and  691 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 691 is 4. 2 are positive, and 2 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 691 by Prime Factorization

The number 691 is a prime 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.prime factorization of 691

Before finding the factors of 691 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 691, 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 691 can be expressed as:

691 = 1 x 691

Factors of 691 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.Factors of 691 in Pairs

For 691, the factor pairs can be found as:

1 x 691 = 691

The possible factor pairs of 691are given as (1,691).

All these numbers in pairs, when multiplied, give 691 as the product.

The negative factor pairs of 691 are given as:

-1 x -691 = 691

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, and -691 are called negative factors of 691.

The list of all the factors of 691, including positive as well as negative numbers, is given below.

Factor list of 691:1, -1, 691, and -691

Factors of 691 Solved Examples

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

Example 1

How many factors of 691 are there?


The total number of Factors of 691 is 4.

Factors of 691 are 1, and 691.

Example 2

Find the factors of 691 using prime factorization.


The prime factorization of 691 is given as:

691 $\div$ 1 = 691

691 $\div$ 691 = 1

So the prime factorization of 691 can be written as:

1 x 691 = 691

Factors of 690|Factors List| Factors of 692