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Factors of 688: Prime Factorization, Methods, and Examples

Numbers that perfectly divide the given number 688 are known as the 688 factors. The component of the number is its factor. 

If the given number is obtained by multiplying two-factor integers, then the factors of the number 688 can be either positive or negative.

Factors of 688

Here are the factors of number 688.

Factors of 688: 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688

Negative Factors of 688

The negative factors of 688 are similar to their positive aspects, just with a negative sign.

Negative Factors of 688: -1, -2, -4, -8, -16, -43, -86, -172, -344, and -688

Prime Factorization of 688

The prime factorization of 688 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 2 x 43

In this article, we will learn about the factors of 688 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 688?

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688. These numbers are the factors as they do not leave any remainder when divided by 688.

The factors of 688 are classified as prime numbers and composite numbers. The prime factors of the number 688 can be determined using the prime factorization technique.

How To Find the Factors of 688?

You can find the factors of 688 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 688, create a list containing the numbers that are exactly divisible by688 with zero remainders. One important thing to note is that 1 and 688 are the 688’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 688 are determined as follows:

\[\dfrac{688}{1} = 688\]

\[\dfrac{688}{2} = 344\]

\[\dfrac{688}{4} = 172\]

\[\dfrac{688}{8} = 86\]

\[\dfrac{688}{16} = 43\]

\[\dfrac{688}{43} = 16\]

\[\dfrac{688}{86} = 8\]

\[\dfrac{688}{172} = 4\]

\[\dfrac{688}{344} = 2\]

\[\dfrac{688}{688} = 1\]

Therefore, 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688are the factors of 688.

Total Number of Factors of 688

For 688, there are 10 positive factors and 10 negative ones. So in total, there are 20 factors of 688. 

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 688 is given as:

Factorization of 688 is 1 x2 x 2 x 2 x 2 x 43.

The exponent of 2 is 4, 1 is 1and  43 is 1.

Adding 1 to each and multiplying them together results in 20.

Therefore, the total number of factors of 688 is 20. 10 are positive, and 10 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 688 by Prime Factorization

The number 688 is a composite/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.

Before finding the factors of 688 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 688, 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 688 can be expressed as:

688 = 2 x 2 x 2 x 2 x 43

Factors of 688 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 688, the factor pairs can be found as:

1 x 688 = 688

2 x 344 = 688

4 x 172  = 688

8 x 86 = 688

16 x 43 = 688

The possible factor pairs of 688 are given as (1, 688),(2, 344),(4, 172)(8, 86), and (16, 43 ).

All these numbers in pairs, when multiplied, give 688 as the product.

The negative factor pairs of 688 are given as:

-1 x -688 = 688

-2 x -344 = 688

-4 x -172  = 688

-8 x -86 = 688

-16 x -43 = 688

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, -4, -8, -16, -43, -86, -172, -344, and -688are called negative factors of 688.

The list of all the factors of 688, including positive as well as negative numbers, is given below.

Factor list of 688:1, -1,2, -2,4, -4, 8,-8,16, -16,43, -43,86, -86,172, -172,344, -344, 688, and -688

Factors of 688 Solved Examples

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

Example 1

How many factors of 688 are there?

Solution

The total number of Factors of 688 is 20.

Factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688.

Example 2

Find the factors of688 using prime factorization.

Solution

The prime factorization of 688 is given as:

688 $\div$ 2 = 344 

344 $\div$ 2 = 172 

172 $\div$ 2 = 86 

86 $\div$ 2 = 43

43 $\div$ 43 = 1

So the prime factorization of 688 can be written as:

2 x 2 x 2 x 2 x 43 = 688

Factors of 687|Factors List| Factors of 689

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