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Factors of 83: Prime Factorization, Methods, Tree, and Examples

Factors of 83 are those numbers that divide the number 83 exactly without leaving any remainder, or it can also be termed as all the numbers that give 83 as a product when multiplied together. 

To get the pair factors of 83, multiply any two natural numbers to get the original number i.e., 83. In the case of 83, there are only two factors as 83 is a prime number. The factors of 83 are 1 and 83, 83 being the highest factor.

In this article, we will be discussing various methods for finding the factors, what is prime factorization and how it is performed for the number 83.

What Are the Factors of 83?

The factors of 83 are 1 and 83 itself.

Factors of 83 are the group of natural numbers or integers that can be divided equally into 83. As 83 is an odd number none of its factors is 2 or any multiple of 2. 83 being a prime number cannot be divided by any other number except for 1 and 83 itself.

How To Calculate the Factors of 83?

To calculate the factors of 83, start dividing it by the smallest natural number 1, and see whether the remainder is zero or not. As for the number to be a factor of the given number, it must be exactly divisible by the number leaving zero as the remainder.

To find the factors of 83, start dividing 83 by the smallest whole number (odd number) and if the result in the remainder is 0, it is a factor of 83. Please keep in mind that 83 is an odd number so odd numbers can only be factors of 83.

Firstly, divide 83 by 1.

\[ \dfrac{83}{1} = 83 \]

Since, the remainder is 0, hence 1 is a factor of 83.

Now, divide 83 by the next odd number in the list of natural numbers which is 3.

\[ \dfrac{83}{3} = 27.666 \]

When we divide 83 by 3; the quotient is 27 and the remainder is 2. Since the remainder is not 0, so 3 is not a factor of 83.

Lastly, divide 83 by 83.

\[ \dfrac{83}{83} = 1 \]

Therefore, 83 is the factor.

A number can have positive as well as negative factors. There are two positive factors of 83 and two negative factors of 83. Positive Factors of 83 are 1, and 83 while negative factors of 83 are -1, and -83.

The factors of 83 can also be found by multiplying two natural numbers to get 83:

\[ 83 \times 1 = 83 \]

So, the factor list of 83 is given below.

Factors List of 83: 1, -1, 83, and -83 

Important Properties

Following mentioned are some important properties of factors of 83:

  1. 83 is an odd number so all of its factors are odd i.e. 1 and 83.
  2. 83 is a prime number, so it has only two factors.
  3. The prime factorization of the number 83 is given as 1 x 83 = 83.
  4. There is only 1 positive factor pair of 83 and 1 negative factor pair of 83.
  5. None of its factors is a decimal or in the form of fractions.

Factors of 83 by Prime Factorization

The prime factorization method is used to find out the factors of 83. Let’s first understand what is prime factorization. Prime factorization is a method of representing the given number as the product of its prime factors. For example, the prime factorization of 4 is 2 * 2 = 4 where 2 is the prime factor of 4.

Similarly in the case of 83, expressing its prime factors in the form of the product is regarded as its prime factorization. As we have discussed earlier 83 has only two factors 1 and 83 therefore the prime factorization of 83 is shown below:

Figure 1

So, the prime factorization of 83 is:

\[ 83 = 1 \times 83 \]

The more interesting facts about factors of 83 are that:

  1. The sum of factors of 83 is an even number.
  2. The product of factors of 83 is an odd number.
  3. 83 can have only 2 factors which are 1 and 83 itself.

Factor Tree of 83

The factor tree of 83 is shown below in figure 2:

Figure 2

As 83 is a prime number so only factors are 1 and 83 as illustrated in the factor tree.

Factors of 83 in Pairs

Any pair of numbers whose product is 83 is called factor pair of 83 in pairs.

The factor pairs are given as:

\[ 83 = 1 \times 83 \]

\[ 83 = 83 \times 1 \]

\[ 83 = -1 \times -83 \]

\[ 83 = -83 \times -1 \]

Hence 83 has only one positive factor pair that is given as (1, 83) or (83, 1).

The negative factor pair of 83 is given as (-1, -83) or (-83, -1).

Factors of 83 Solved Examples

Let’s solve some detailed examples to better understand the methods used for finding the factors of 83.

Example 1

What is the Highest Common Factor (HCF) of 83 and 42?

Solution

The factors of 83 are 1 and 83.

Factors of 42 are 1, 2, 3, 7, and 42.

The common factor of 83 and 42 is 1.

So, the Highest Common Factor (HCF) of 83 and 42 is 1.

Example 2

List the negative factors of 83.

Solution

The negative factors of 83 are -1 and -83.

It has only two factors as 83 is a prime number.

Factors are the integers that when multiplied together give the number as the product whose factors are to be found.

Similarly when -1 and -83 are multiplied the product is 83 as shown:

\[ -1 \times -83 = 83 \]

So, -1 and -83 are negative factors of 83.

Example 3

Hana’s tutor gave her an activity to find out the Least Common Multiple (LCM) of 83 and 24. How her elder brother will help her to find the LCM.

Solution

Hana’s brother will first find out the factors of 83 and 24.

Prime Factors of 83 are 1,83.

Prime Factors of 24 are the following: 2,2,2,3.

Hence the LCM will be given as:

\[ L.C.M = 2 \times 2 \times 2 \times 3 \times 83 \]

\[ L.C.M = 1992 \]

So, the LCM of 83 and 24 is 1992.

Images/mathematical drawings are created with GeoGebra. 

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