# Factors of 99

Factors of 99 are 1, 3, 9, 11, 33, and 99

#### How to find factors of a number

 1.   Find factors of 99 using Division Method 2.   Find factors of 99 using Prime Factorization 3.   Find factors of 99 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 99

• Divide 99 by 1: 99 ÷ 1 : Remainder = 0
• Divide 99 by 3: 99 ÷ 3 : Remainder = 0
• Divide 99 by 9: 99 ÷ 9 : Remainder = 0
• Divide 99 by 11: 99 ÷ 11 : Remainder = 0
• Divide 99 by 33: 99 ÷ 33 : Remainder = 0
• Divide 99 by 99: 99 ÷ 99 : Remainder = 0

Hence, Factors of 99 are 1, 3, 9, 11, 33, and 99

#### 2. Steps to find factors of 99 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 99 using the division method, follow these steps:

• Step 1. Start dividing 99 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 99, which is 3. Divide 99 by 3 to obtain the quotient (33).
99 ÷ 3 = 33
• Step 3. Repeat step 1 with the obtained quotient (33).
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 99 is, 99 = 3 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 99 as shown below:

So, the prime factorization of 99 is, 99 = 3 x 3 x 11.

#### 3. Find factors of 99 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 99 would be the two numbers which, when multiplied, give 99 as the result.

The following table represents the calculation of factors of 99 in pairs:

Factor Pair Pair Factorization
1 and 99 1 x 99 = 99
3 and 33 3 x 33 = 99
9 and 11 9 x 11 = 99

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 99. They are called negative pair factors.

Hence, the negative pairs of 99 would be ( -1 , -99 ) , ( -3 , -33 ) and ( -9 , -11 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every number is a factor of zero (0), since 99 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 11, 33, 99 are exact divisors of 99.
• Factors of 99 are 1, 3, 9, 11, 33, 99. Each factor divides 99 without leaving a remainder.

• Which is the smallest prime factor of 99?

Smallest prime factor of 99 is 3.

• Is 99 a perfect square?

No 99 is not a perfect square.

• What are five multiples of 99?

First five multiples of 99 are 198, 297, 396, 495, 594.

• What is prime factorization of 99?

Prime factorization of 99 is 3 x 3 x 11.

• What are factors of 99?

Factors of 99 are 1, 3, 9, 11, 33, 99.

• How do you find factors of a negative number? ( eg. -99 )?

Factors of -99 are -1, -3, -9, -11, -33, -99.

• Is 99 a whole number?

Yes 99 is a whole number.

• Which is greatest factor of 99?

The greatest factor of 99 is 33.

• What are the prime factors of 99?

The factors of 99 are 1, 3, 9, 11, 33, 99.
Prime factors of 99 are 3, 3, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 99. Can you help her?

Prime factors of 99 are 3, 3, 11.
Hence, the product of prime factors of 33.

Can you help Rubel to find out the product of the even factors of 99?

Factors of 99 are 1, 3, 9, 11, 33, 99.
Even factors of 99 are 0.
Hence, product of even factors of 99 is; 0 = 0.

Joy wants to calculate mean of all the factors of 99. Help him in finding the mean of 99.

Factors of 99 are 1, 3, 9, 11, 33, 99.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 99 is 1 + 3 + 9 + 11 + 33 + 99 = 156.
Hence, the mean of factors of 99 is 156 ÷ 6 = 26.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 99? Help her in writing all the factors.

Positive factors are 1, 3, 9, 11, 33, 99.
Negative factors are -1, -3, -9, -11, -33, -99.

How many factors are there for 99?

Factors of 99 are 1, 3, 9, 11, 33, 99.
So there are in total 6 factors.

Joey wants to write all the prime factors of 99 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 99 are 3, 3, 11.
So in exponential form it can be written as 32 x 11.

Kevin has been asked to write 5 factor(s) of 99. Can you predict the answer?

5 factor(s) of 99 are 1, 3, 9, 11, 33.