How to Find and List All the Factors of 18 Step by Step
The concept of factors of 18 is a key foundation of mathematics. Being able to quickly find all the factors of 18 is not only vital for MCQ exams and homework but also helps with learning other concepts like LCM, HCF, divisibility, and factorization. This page at Vedantu is designed to be a stepwise, mobile-orientated guide for students of all levels.
What Are Factors of 18?
A factor of 18 is any whole number that divides 18 exactly without leaving any remainder. In other words: the result of 18 divided by that number is also a whole number. You’ll see factors of 18 show up in questions on divisibility, HCF/LCM (Highest Common Factor/Lowest Common Multiple), and prime factorization often throughout Maths.
Key Formula for Factors of 18
There’s no single "formula," but the standard method to find factors is:
Try all integers from 1 up to 18. If 18 ÷ n is a whole number (no remainder), that n is a factor.
In symbols: Find all n where \( 18 \div n = \) whole number.
List of All Factors of 18
The factors of 18 are: 1, 2, 3, 6, 9, 18
Each of these divides 18 perfectly (for example, 18 ÷ 3 = 6, with no remainder). Negative numbers can also be factors (like –2, –3, etc.), but usually positive factors are preferred for school and exam questions.
Step-by-Step Illustration: How to Find Factors of 18
-
Start with 1.
18 ÷ 1 = 18 (1 is a factor) -
Next, try 2.
18 ÷ 2 = 9 (2 is a factor) -
Try 3.
18 ÷ 3 = 6 (3 is a factor) -
Try 4.
18 ÷ 4 = 4.5 (fraction — so 4 is NOT a factor) -
Try 5.
18 ÷ 5 = 3.6 (fraction — not a factor) -
Try 6.
18 ÷ 6 = 3 (6 is a factor) -
Similarly, try 7, 8 (not factors).
Try 9.
18 ÷ 9 = 2 (9 is a factor) -
Try numbers up to 18.
18 ÷ 18 = 1 (18 is a factor)
Factor Pairs of 18 (Table)
| Factor 1 | Factor 2 | Explanation |
|---|---|---|
| 1 | 18 | 1 × 18 = 18 |
| 2 | 9 | 2 × 9 = 18 |
| 3 | 6 | 3 × 6 = 18 |
So, the factor pairs of 18 are: (1, 18), (2, 9), and (3, 6).
Prime Factorization of 18
To express 18 as a product of only prime numbers, break it down step by step:
- Divide 18 by 2 (smallest prime): 18 ÷ 2 = 9
- Divide 9 by 3 (next smallest prime): 9 ÷ 3 = 3
- Divide 3 by 3: 3 ÷ 3 = 1
So, prime factorization of 18 = 2 × 3 × 3 (or \( 2 \times 3^2 \)).
You can also show this with a simple factor tree diagram in class.
Speed Trick for Exams
Here’s a quick trick: count the number itself (1 and 18), then test each number up to its square root (about 4.2 for 18). If 18 ÷ n is whole, n and 18 ÷ n are both factors! This halves your work for MCQs. Vedantu’s live classes often teach such examination shortcuts for time-savings.
Cross-Disciplinary Usage
Knowing the factors of 18 helps you in Maths for topics like LCM and HCF. It also appears in divisibility tests, simplifying fractions, solving number puzzles in computer science, and logical reasoning for Olympiads and JEE/NEET preparation.
Relation to Other Concepts
Understanding factors of 18 also helps see patterns with factors of 12 or factors of 24. You’ll spot how common factors relate to LCM, HCF, and even divisibility — a foundation for more advanced topics.
Factors of 18 vs Nearby Numbers (Quick Comparison Table)
| Number | All Factors |
|---|---|
| 12 | 1, 2, 3, 4, 6, 12 |
| 18 | 1, 2, 3, 6, 9, 18 |
| 20 | 1, 2, 4, 5, 10, 20 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 30 | 1, 2, 3, 5, 6, 10, 15, 30 |
Classroom Tip
A quick way to remember factors of 18: use multiplication tables for 1, 2, 3, and so on, and see what makes 18! Example: 3 × 6, 2 × 9, 1 × 18. Vedantu’s teachers encourage drawing “factor pair ladders” as a fast visual method for recall.
Try These Yourself
- List all factors of 18 and write them as pairs.
- What are the factors of 36?
- Which numbers between 10 and 20 are factors of 18?
- Is 24 a factor of 18? Why or why not?
- Find the prime factorization of 18 (show your steps).
Frequent Errors and Misunderstandings
- Forgetting that “factors” means “divides exactly.”
- Mixing up factors and multiples (for example, listing 36 as a “factor” of 18 — which it’s not!)
- Missing one or more pairs (e.g., skipping 9 as a factor).
Wrapping It All Up
We explored factors of 18—from stepwise definition and listing out factor pairs, to prime factorization, applications, and key mistakes. Keep practicing these with class exercises or Vedantu's live help, and try similar questions on factors of any number or prime factorization methods to master exam basics!
Related Pages to Explore
FAQs on Factors of 18 with Factor Pairs and Prime Factorization
1. What are the factors of 18?
The factors of 18 are the whole numbers that divide 18 without leaving a remainder. These are 1, 2, 3, 6, 9, and 18. They can also be negative: -1, -2, -3, -6, -9, and -18.
2. How do you find all factors of 18?
To find all factors, systematically divide 18 by each whole number starting from 1, until you reach 18. If the division results in a whole number, that number is a factor. You can also consider negative integer divisors.
3. What are the factor pairs of 18?
Factor pairs are sets of two numbers that multiply to give 18. The positive factor pairs of 18 are: (1, 18), (2, 9), and (3, 6). Including negative factors, you would also have (-1,-18), (-2,-9), and (-3,-6).
4. What is the prime factorization of 18?
Prime factorization expresses a number as a product of prime numbers. The prime factorization of 18 is 2 x 3 x 3 or 2 x 32.
5. Is 24 a factor of 18?
No, 24 is not a factor of 18 because 18 divided by 24 does not result in a whole number.
6. What is a factor tree, and how can I use it to find the factors of 18?
A factor tree is a visual method to find the prime factorization of a number. Start with 18. Find two factors (e.g., 2 and 9). If a factor is not prime, break it down further (9 = 3 x 3). Continue until all branches end in prime numbers. The prime factors at the end of the branches (2, 3, and 3) make up the prime factorization of 18.
7. How are factors of 18 used in finding the Highest Common Factor (HCF)?
To find the HCF of 18 and another number, list the factors of both numbers. The largest factor common to both lists is the HCF. For example, to find the HCF of 18 and 24, the factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The highest common factor is 6.
8. How are factors of 18 used in finding the Lowest Common Multiple (LCM)?
Finding the LCM involves using the prime factorization of the numbers involved. First, find the prime factorization of 18 (2 x 32) and the prime factorization of the other number. The LCM is found by taking the highest power of each prime factor present in either factorization.
9. What is the difference between factors and multiples?
Factors divide a number evenly, while multiples are the result of multiplying a number by an integer. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18, while some multiples of 18 are 18, 36, 54, and 72.
10. Can negative numbers be considered factors?
Yes, negative numbers can also be factors. For example, -1 and -18 are factors of 18 because (-1) x (-18) = 18. However, factor lists usually only show positive factors for simplicity.
11. How many factors does the number 18 have?
The number 18 has a total of 6 positive factors (1, 2, 3, 6, 9, 18) and 6 negative factors (-1, -2, -3, -6, -9, -18), making a total of 12 factors.
