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# Factors of 93: Prime Factorization, Methods, Tree, and Examples

**Factors of 93**are the numbers that can be divided by 93 without leaving any remainder. For the factors, the condition is that they must be

**exactly divisible**by the given number or must have

**zero**as a remainder when divided. Factors are also known as

**divisors**of the given number.

Figure 1 – All possible factors of 93

In this article, we will be finding the**factors of 93**. There are several ways to find factors of any number. We are going to learn how to find factors by the

**division method**. After reading this article, you will have a clear understanding of

**prime factorization**, prime numbers, and factor pairs by using positive and negative factors and a factor tree. In the end, there are some examples for better understanding and your practice.

## What Are the Factors of 93?

**The factors of 93 are 1, 3, 31, and 93, as all of them are exactly divisible by 93.**The numbers that can

**completely divide**93 are included in the list of its factors. In other words, the

**remainder**should always be

**zero**. The given number 93 is not a prime number so it has more than 2 factors. It has both positive and negative factors although negative factors are not often considered. 93 has

**four factors**in total. A number that has more than 2 factors is known as a composite number.

## How To Calculate the Factors of 93?

To calculate the factors of 93, divide it by the smallest natural number which is 1.**1**is a factor of all the whole numbers because it divides every number completely which means the remainder is zero.\[ \dfrac{93}{1} = 93,\ r = 0 \]As a result, 1 will be included in the factors list of 93.93 is an

**odd number,**so it cannot be divided by 2. So, we will determine its smallest prime factor which is 3. Now, divide 93 by 3.\[ \dfrac{93}{3} = 31 \]This means 3 and 31 both are factors of 93 because both divide 93 completely and the remainder is zero in both cases.Check for the other

**natural numbers**as well.Dividing 93 by 6 gives:\[ \dfrac{93}{6} =15.5 \]The remainder is 3, which is a non-zero number so 6 is not a factor of 93.Now divide 93 by 9:\[ \dfrac{93}{9}=10.33 \]The remainder is 3, which is also a non-zero number so 9 is also not a factor of 93.The last factor will be the number itself because every number divides

**itself**fully.Following are the numbers that entirely divide the

**number 93**without leaving any remainder.\[ \dfrac{93}{1} = 93 \]\[ \dfrac{93}{3} = 31 \]\[ \dfrac{93}{31} = 3 \]\[ \dfrac{93}{93} = 1 \]The

**positive**and

**negative factors**of 93 are listed below:

**Positive factors**are 1, 3, 31, and 93.

**Negative factors**are -1, -3, -31, and -93.

### Properties of Factors of 93

Following are some important properties of factors of 93:- 93 is an
**odd number**therefore, it has no even prime factor. - The factor of 93 can never be in the form of a
**decimal**or**fraction**. - 93 is a
**semiprime.**Semiprime is the natural number that is the product of two prime numbers. - 93 is also the first natural number in the
**third triples of successive semiprime numbers.**The triplet is 93, 94, and 95. - The
**additive inverse**of every factor of 93 is also its factor which is called a negative factor.

## Factors of 93 by Prime Factorization

**Prime numbers**are the numbers that have only 2 factors. Those two factors are 1 and the other is the number itself. For example: 2,3,5,7,11….31 etc.(NOTE: 0 and 1 are not prime numbers)

**Prime Factorization**means representing numbers by the product of their prime factors. The

**list of prime factors**contains the factors which are prime numbers. This is an important topic. As mentioned above in the article factors of 93 are

**1, 3, 31, & 93.**The numbers

**3**and

**31**are prime numbers because they are not divisible on any number completely except for 1 and itself. So the prime factorization of 93 is 3 x 31. It can be expressed as:

**93 = 3 x 31 **

## Factor Tree of 93

The**factor tree of 93**is shown below in figure 1:

Figure 2 – Factor tree of 93

This diagram is known as a factor tree. The factor tree consists of factors of the number. At the top of the factor tree, each branch will contain its factors. It is a pictorial representation of factors of the given number.By looking at the factor tree, one could easily understand that by multiplying 3 and 31 we will get the original number which is 93.## Factors of 93 in Pairs

Pairing the factors of a number means writing them in such pairs that the**product must be equal to the number itself**.

** 3× 31=93**

**1× 93=93 **

**(3, 31)**and

**(1, 93)**.We can also find factor pairs with negative factors of 93

**-3×- 31=93 **

**-1× -93=93 **

**(-1, -93),**and

**(-3, -31).**When a negative sign is multiplied by a negative sign their product is always positive.

## Factors of 93 Solved Examples

Following are some solved examples related to factors of 93.### Example 1

Find the sum of all factors of 93.### Solution

Factors of 93 are**1, 3, 31,**and

**93.**Add up all the factors to find the sum.Sum of all factors of 93 is given as:

**Sum = 1 + 3 + 31 + 93**

**Sum = 128**

### Example 2

Find the common factors of 93 and 3.### Solution

Factors of 93 are**1, 3, 31,**and

**93.**As we know 3 is a prime number so it will have only 2 factors 1 and the number itself Factors of 3 are

**1**and

**3**.Common factors mean factors that are part of both lists.Common factors of 3 and 93 are 1 and 3.

### Example 3

Find the negative factor pair of 93.### Solution

Negative factors of 93 are -1, -3, -31and -93.The first Factor pair will be (-1, -3).The second Factor pair will be (-31, -93).Negative factor pair of 93 are**(-1, -3)**and

**(-31, -93)**

*Images/mathematical drawings are created with GeoGebra.*