# Factors of 198

Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198

#### How to find factors of a number

 1.   Find factors of 198 using Division Method 2.   Find factors of 198 using Prime Factorization 3.   Find factors of 198 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 198

• Divide 198 by 1: 198 ÷ 1 : Remainder = 0
• Divide 198 by 2: 198 ÷ 2 : Remainder = 0
• Divide 198 by 3: 198 ÷ 3 : Remainder = 0
• Divide 198 by 6: 198 ÷ 6 : Remainder = 0
• Divide 198 by 9: 198 ÷ 9 : Remainder = 0
• Divide 198 by 11: 198 ÷ 11 : Remainder = 0
• Divide 198 by 18: 198 ÷ 18 : Remainder = 0
• Divide 198 by 22: 198 ÷ 22 : Remainder = 0
• Divide 198 by 33: 198 ÷ 33 : Remainder = 0
• Divide 198 by 66: 198 ÷ 66 : Remainder = 0
• Divide 198 by 99: 198 ÷ 99 : Remainder = 0
• Divide 198 by 198: 198 ÷ 198 : Remainder = 0

Hence, Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198

#### 2. Steps to find factors of 198 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 198 using the division method, follow these steps:

• Step 1. Start dividing 198 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 198, which is 2. Divide 198 by 2 to obtain the quotient (99).
198 ÷ 2 = 99
• Step 3. Repeat step 1 with the obtained quotient (99).
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 198 is, 198 = 2 x 3 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 198 as shown below:

So, the prime factorization of 198 is, 198 = 2 x 3 x 3 x 11.

#### 3. Find factors of 198 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 198 would be the two numbers which, when multiplied, give 198 as the result.

The following table represents the calculation of factors of 198 in pairs:

Factor Pair Pair Factorization
1 and 198 1 x 198 = 198
2 and 99 2 x 99 = 198
3 and 66 3 x 66 = 198
6 and 33 6 x 33 = 198
9 and 22 9 x 22 = 198
11 and 18 11 x 18 = 198

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 198. They are called negative pair factors.

Hence, the negative pairs of 198 would be ( -1 , -198 ) , ( -2 , -99 ) , ( -3 , -66 ) , ( -6 , -33 ) , ( -9 , -22 ) and ( -11 , -18 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 198 is a factor of itself.
• 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, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 are exact divisors of 198.
• 1 is a factor of every number. Eg. 1 is a factor of 198.
• Every number is a factor of zero (0), since 198 x 0 = 0.

• Which is the smallest prime factor of 198?

Smallest prime factor of 198 is 2.

• Is 198 a perfect square?

No 198 is not a perfect square.

• What are five multiples of 198?

First five multiples of 198 are 396, 594, 792, 990, 1188.

• What is prime factorization of 198?

Prime factorization of 198 is 2 x 3 x 3 x 11.

• What are factors of 198?

Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.

• How do you find factors of a negative number? ( eg. -198 )?

Factors of -198 are -1, -2, -3, -6, -9, -11, -18, -22, -33, -66, -99, -198.

• Is 198 a whole number?

Yes 198 is a whole number.

• Which is greatest factor of 198?

The greatest factor of 198 is 99.

• What are the prime factors of 198?

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
Prime factors of 198 are 2, 3, 3, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 198. Can you help her?

Prime factors of 198 are 2, 3, 3, 11.
Hence, the product of prime factors of 66.

Can you help Rubel to find out the product of the even factors of 198?

Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
Even factors of 198 are 2, 6, 18, 22, 66, 198.
Hence, product of even factors of 198 is; 2 x 6 x 18 x 22 x 66 x 198 = 62099136.

Joy wants to calculate mean of all the factors of 198. Help him in finding the mean of 198.

Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 198 is 1 + 2 + 3 + 6 + 9 + 11 + 18 + 22 + 33 + 66 + 99 + 198 = 468.
Hence, the mean of factors of 198 is 468 ÷ 12 = 39.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 198? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
Negative factors are -1, -2, -3, -6, -9, -11, -18, -22, -33, -66, -99, -198.

How many factors are there for 198?

Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
So there are in total 12 factors.

Joey wants to write all the prime factors of 198 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 198 are 2, 3, 3, 11.
So in exponential form it can be written as 2 x 32 x 11.

Kevin has been asked to write 11 factor(s) of 198. Can you predict the answer?

11 factor(s) of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99.