# Factors of 18

Factors of 18 are 1, 2, 3, 6, 9, and 18

#### How to find factors of a number

 1.   Find factors of 18 using Division Method 2.   Find factors of 18 using Prime Factorization 3.   Find factors of 18 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 18

• Divide 18 by 1: 18 ÷ 1 : Remainder = 0
• Divide 18 by 2: 18 ÷ 2 : Remainder = 0
• Divide 18 by 3: 18 ÷ 3 : Remainder = 0
• Divide 18 by 6: 18 ÷ 6 : Remainder = 0
• Divide 18 by 9: 18 ÷ 9 : Remainder = 0
• Divide 18 by 18: 18 ÷ 18 : Remainder = 0

Hence, Factors of 18 are 1, 2, 3, 6, 9, and 18

#### 2. Steps to find factors of 18 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 18 using the division method, follow these steps:

• Step 1. Start dividing 18 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 18, which is 2. Divide 18 by 2 to obtain the quotient (9).
18 ÷ 2 = 9
• Step 3. Repeat step 1 with the obtained quotient (9).
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 18 is, 18 = 2 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 18 as shown below:

So, the prime factorization of 18 is, 18 = 2 x 3 x 3.

#### 3. Find factors of 18 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 18 would be the two numbers which, when multiplied, give 18 as the result.

The following table represents the calculation of factors of 18 in pairs:

Factor Pair Pair Factorization
1 and 18 1 x 18 = 18
2 and 9 2 x 9 = 18
3 and 6 3 x 6 = 18

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 18. They are called negative pair factors.

Hence, the negative pairs of 18 would be ( -1 , -18 ) , ( -2 , -9 ) and ( -3 , -6 ) .

#### 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. 18 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, 18 are exact divisors of 18.
• 1 is a factor of every number. Eg. 1 is a factor of 18.
• Every number is a factor of zero (0), since 18 x 0 = 0.

• Which is the smallest prime factor of 18?

Smallest prime factor of 18 is 2.

• Is 18 a perfect square?

No 18 is not a perfect square.

• What are five multiples of 18?

First five multiples of 18 are 36, 54, 72, 90, 108.

• What is prime factorization of 18?

Prime factorization of 18 is 2 x 3 x 3.

• What are factors of 18?

Factors of 18 are 1, 2, 3, 6, 9, 18.

• How do you find factors of a negative number? ( eg. -18 )?

Factors of -18 are -1, -2, -3, -6, -9, -18.

• Is 18 a whole number?

Yes 18 is a whole number.

• Which is greatest factor of 18?

The greatest factor of 18 is 9.

• What are the prime factors of 18?

The factors of 18 are 1, 2, 3, 6, 9, 18.
Prime factors of 18 are 2, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 18. Can you help her?

Prime factors of 18 are 2, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 18?

Factors of 18 are 1, 2, 3, 6, 9, 18.
Even factors of 18 are 2, 6, 18.
Hence, product of even factors of 18 is; 2 x 6 x 18 = 216.

Joy wants to calculate mean of all the factors of 18. Help him in finding the mean of 18.

Factors of 18 are 1, 2, 3, 6, 9, 18.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 18 is 1 + 2 + 3 + 6 + 9 + 18 = 39.
Hence, the mean of factors of 18 is 39 ÷ 6 = 6.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 18? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18.
Negative factors are -1, -2, -3, -6, -9, -18.

How many factors are there for 18?

Factors of 18 are 1, 2, 3, 6, 9, 18.
So there are in total 6 factors.

Joey wants to write all the prime factors of 18 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 18 are 2, 3, 3.
So in exponential form it can be written as 2 x 32.

Kevin has been asked to write 5 factor(s) of 18. Can you predict the answer?

5 factor(s) of 18 are 1, 2, 3, 6, 9.