18 is the only number where the sum of its written digits (1+8 = 9) is equal to half of itself (18 ÷ 9 = 2). In this lesson, we will calculate the factors of 18, prime factors of 18, and factors of 18 in pairs along with solved examples for a better understanding.

**Factors of 18:**1, 2, 3, 6, 9, and 18**Prime Factorization of 18:**2 × 3 × 3 = 2 × 3^{2}

Let us explore more about factors of 18 and ways to find them.

**Table of Content**

- What Are the Factors of 18?
- How to Calculate Factors of 18?
- Factors of 18 in Pairs
- Important Notes
- FAQs on Factors of 18
- Factors of 18 Solved Examples
- Challenging Questions
- Interactive Questions

## What Are the Factors of 18?

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, the factors of 18 are 1, 2, 3, 6, 9, and 18. So,18 is a composite number as it has more factors other than 1 and itself.

## How to Calculate Factors of 18?

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 18. In prime factorization, we express 18 as a product of its prime factors, and in the division method, we see which numbers divide 18 exactly without a remainder.

Let us calculate factors of 18 using following two methods:

- Factors of 18 by prime factorization factor tree method
- Factors of 18 by upside-down division method

### Prime Factorization By Upside-Down Division Method

Prime factorization is expressing a number as a product of its factors which are prime.

For example, factors of 6 are 1, 2, 3, 6

6 = 2 × 3

So, the prime factors of 6 are 2 and 3.

The upside-down division got its name because the division symbol is flipped upside down.

- STEP 1: By using divisibility rules, we find out the smallest exact prime divisor (factor) of the given number. Here, 18 is an even number. So it is divisible by 2. In other words, 2 divides 18 with no remainder. Therefore, 2 is the smallest prime factor of 18.
- STEP 2: We divide the given number by its smallest factor other than 1 (prime factor), 18 ÷ 2 = 9
- STEP 3: We then find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 9 is the quotient, 9 ÷ 3= 3
- 3 is the quotient, so we stop the process here. Therefore,
**18 = 2 × 3 × 3**

### Prime Factorization by Factor Tree Method

First, we identify the two factors that give 18. 18 is the root of this factor tree.

18 = × 6

Here, 6 is a composite number. So it can be further factorized.

6 = 3 × 2

We continue this process until we are left with only prime numbers, i.e., till we cannot further factor the obtained numbers.

We then circle all the prime numbers in the factor tree. Basically, we branch out 18 into its prime factors.

So, prime factorization of 18 is 18= 2 × 3 × 3.

A factor tree is not unique for a given number. Instead of expressing 18 as 2 × 9, we can express 18 as 3 × 6. Here is a simple activity to try on your own. Instead of 2 × 9, if I had used 3 × 6, do you think we would get the same factors?

Can you draw the factor tree with 3 and 6 as the branches?

**Explore factors using illustrations and interactive examples**

- Factors of 17: The factors of 17 are 1 and 17.
- Factors of 12: The factors of 12 are 1, 2, 3, 4, 6, and 12.
- Factors of 19: The factors of 19 are 1 and 19.
- Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
- Factors of 13: The factors of 13 are 1 and 13.

## Factors of 18 in Pairs

Factor pairs are the two numbers which, when multiplied, give the number 18.

- 18 = 1 × 18
- 18 = 2 × 9
- 18 = 3 × 6

Therefore, pair factors of 18 are (1,18), (2,9), and (3,6). A factor rainbow helps you find all of the factors. It is called a rainbow because all of the factor pairs connect to make a rainbow! Making a factor rainbow is quite easy.

Let’s try one:

Find all of the factors for the number 18.

- Step I: Start with 1 and the number itself.
- Step II: Count up by ones to see if you can multiply two numbers together to get your target number.
- Step III: Stop when you can’t get any more numbers in between.
- Step IV: Connect the factor pairs.

In total, we have 3 factor pairs, i.e., there are 6 factors of 18: 1, 2, 3, 6, 9, 18.

**We can have negative factors also for a given number.**

For example:

Since the product of two negative numbers is positive [(-) × (-) = +].

(-1,-18) , (-2,-9), and (-3,-6) are also factor pairs of 18.

But for now, let us focus on the positive factors in this article.

With factors, we are only looking for whole numbers that are equal to or less than the original number.

**Important Notes:**

- Factors of a number are the numbers that divide the given number exactly without any remainder.
- 18 is a composite number as it has more factors other than 1 and itself.
- Pair factors of 18 are (1,18), (2,9), and (3,6).
- 1 is a factor of every number.
- The factor of a number is always less than or equal to the given number.
- Prime factorization is expressing the number as a product of its factors which are prime.

## FAQs on Factors of 18

### What are the prime factors of 18?

The prime factors of 18 are 2 and 3. 2 is the smallest prime factor of 18.

### Is 18 a square number?

A perfect square is a number that can be expressed as the product of two equal integers.

As 18 cannot be expressed as the product of two equal numbers,18 is not a square number.

### Which is the smallest factor of 18?

1 is the smallest factor of 18. 2 is the smallest prime factor of 18.

### Which is the highest factor of 18?

18 is the highest factor of 18. Every number is the highest factor of itself.

### What are the common factors of 18 and 6?

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

Factors of 6 are 1, 2, 3, and 6.

The common factors of 18 and 6 are 1, 2, 3, and 6.

## Solved Examples

**Example 1: **List out the factors of 18 and its factor pairs.

**Solution:**

- 18 = 1 × 18
- 18 = 2 × 9
- 18 = 3 × 6

Therefore, factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 18 in pairs are (1,18), (2,9), and (3,6).

**Example 2: **There are 18 people in a room together at a party. Everyone would like to take part in games during the party. What could be the possible sizes of groups we can break the people into so that no one is left out and everyone can play?

**Solution:**

To solve this problem, we need to know the factors of 18.

List them out: 1, 2, 3, 6, 9, 18.

Let's see how the factor pairs can help us.

Factor pairs: (1,18), (2,9), (3,6)

- The first pair, 1 and 18, doesn't tell us much. It just means that we could have 1 group of 18.
- The second pair tells us we could have 2 groups of 9 or 9 groups of 2.
- The third pair tells us we could have 3 groups of 6 or 6 groups of 3.

Now we can see that there are three possible combinations for grouping the party guests: (1,18), (2,9), (3,6).

**Example 3: **Xin has a plot of land with an area of 18 sq. ft. He wants to break this plot of land into different equal-sized sections to plant different vegetables. In how many can he devide the plot?

**Solution:**

The area of the rectangle is length × breadth.

Given area = 18 square feet

So, the possible length and breadth are the factor pairs (as the product of these pairs is 18).

Length | Breadth |

1 | 18 |

2 | 9 |

3 | 6 |

There are 3 possible ways. We can swap the dimensions of length and breadth according to situation.

**Challenging Questions:**

- 90 × 0.2= 18. Can we conclude (90, 0.2) as a factor pair of 18?
- Is the number of factors of a given number finite?
- Can the factor of a number be greater than the number itself?

## Interactive Questions

**Here are a few activities for you to practice.**

**Select/Type your answer and click the "Check Answer" button to see the result.**