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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.Â

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**.Â 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.Â

## 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**areÂ 1, 3, 31, and 93.

**Negative factors**areÂ -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 notÂ 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.Â 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 ofÂ 93 is 3 x 31. It can be expressed as:

**93 = 3 x 31Â **

## 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**.

**Â 3Ã— 31=93**

**1Ã— 93=93Â **

**(3, 31)**and

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

**-3Ã—- 31=93Â **

**-1Ã— -93=93Â **

**(-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 itselfÂ Factors of 3 are

**1**and

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

### Example 3

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

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

**(-31, -93)**

*Images/mathematical drawings are created with GeoGebra.*

**Factors Of 91 | All Factors | Factors Of 94**

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