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Factors of 689: Prime Factorization, Methods, and Examples

The whole number that separates the number 689 is one of the components. The number 689 is composite and odd. It recommends there are more than two contributing factors. 

Notwithstanding the signs of the components, duplicating any two numbers components produces the result.

Factors of 689

Here are the factors of number 689.

Factors of 689 : 1, 13, 53 and 689

Negative Factors of 689

The negative factors of 689  are similar to their positive aspects, just with a negative sign.

Negative Factors of 689 : -1, -13, -53 and -689

Prime Factorization of 689

The prime factorization of 689  is the way of expressing its prime factors in the product form.

Prime Factorization: 131 x 531

In this article, we will learn about the factors of 689 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 689?

The factors of 688 are 1, 13, 53 and 689 . These numbers are the factors as they do not leave any remainder when divided by 689.

The factors of 689  are classified as prime numbers and composite numbers. The prime factors of the number 689 can be determined using the prime factorization technique.

How To Find the Factors of 689?

You can find the factors of 689 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 689, create a list containing the numbers that are exactly divisible by 689 with zero remainders. One important thing to note is that 1 and 689 are the 689’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 689 are determined as follows:

\[\dfrac{689}{1} = 689\]

\[\dfrac{689}{13} = 53\]

\[\dfrac{689}{53} = 13\]

\[\dfrac{689}{689} = 1\]

Therefore,1, 13, 53, and 689 are the factors of 689.

Total Number of Factors of 689

For 689, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 689. 

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 689 is given as:

Factorization of 689 is 131 x 531.

The exponent of 13 and  53 is 1.

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

Therefore, the total number of factors of 689 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 689 by Prime Factorization

The number 689  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 689 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 689, 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 689 can be expressed as:

689 = 131 x 531

Factors of 689 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 689, the factor pairs can be found as:

1 x 689 = 689

13 x 53 = 689

The possible factor pairs of 689 are given as (1, 689), and (13, 53 ).

All these numbers in pairs, when multiplied, give 689 as the product.

The negative factor pairs of 689 are given as:

-1 x -689 = 689

-13 x -53 = 689

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, -13, -53, and -689 are called negative factors of 689.

The list of all the factors of 689, including positive as well as negative numbers, is given below.

Factor list of 689: 1,-1, 13,-13, 53, -53 , 689, and -689

Factors of 689 Solved Examples

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

Example 1

How many factors of 689 are there?

Solution

The total number of Factors of689  is 8.

Factors of 689 are 1, 13, 53, and 689.

Example 2

Find the factors of 689 using prime factorization.

Solution

The prime factorization of689 is given as:

689 $\div$ 13 = 53 

53 $\div$ 53 = 1

So the prime factorization of 689 can be written as:

131 x 531 = 689

Factors of 688|Factors List| Factors of 690

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