FactorsAbout 18
18 is twice a square (2 × 9). Its factors include 2 and 9, so the divisibility rules for both apply to it.
Factor pairs of 18
A factor pair is two numbers that multiply to give 18: 1 × 18, 2 × 9 and 3 × 6. Each pair is a way of arranging 18 things in equal rows, so 18 tiles can be laid out as a rectangle in 3 different shapes.
How to find the factors of 18 by hand
Divide 18 by 1, 2, 3 and so on. Each time the division is exact, you have found two factors at once: the divisor and the answer. You can stop at 4, because the next number, 5, gives 5 × 5 = 25, which is more than 18: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 18? | Result |
|---|---|---|
| 1 | yes | 1 × 18 |
| 2 | yes | 2 × 9 |
| 3 | yes | 3 × 6 |
| 4 | no | remainder 2 |
The only number that fails is 4. All the others give a pair.
Prime factorisation of 18
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 18 = 2 × 3 × 3, which is written 2 × 32 with powers. Its prime factors are 2 and 3.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (1 + 1) × (2 + 1) = 6. This works because a factor of 18 can use each prime anywhere from zero times up to its full power.
The 6 factors add up to 39. Leaving out 18 itself, the rest add up to 21, which is more than 18, so 18 is an abundant number. Of its factors, 3 are odd: 1, 3 and 9.
Divisibility rules applied to 18
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 8, which is even.
- By 3: yes. The digits add up to 1 + 8 = 9, which is a multiple of 3.
- By 4: no. The last two digits make 18, and 18 ÷ 4 leaves remainder 2.
- By 5: no. The last digit is 8, not 0 or 5.
- By 6: yes. A number divides by 6 when it divides by both 2 and 3. Here both tests pass.
- By 8: no. 18 ÷ 8 leaves remainder 2.
- By 9: yes. The digits add up to 9, which is a multiple of 9.
- By 10: no. The last digit is not 0.
- By 11: no. Adding alternate digits from the right gives 8 and 1. Their difference is 7, which is not 0 or a multiple of 11.
HCF and LCM with 18
18 and 16. 18 = 2 × 32 and 16 = 24. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 144. By division: 18 = 16 × 1 + 2; 16 = 2 × 8 + 0, so the last divisor, 2, is the HCF. Check: 2 × 144 = 288 = 18 × 16.
18 and 20. 18 = 2 × 32 and 20 = 22 × 5. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 180. By division: 20 = 18 × 1 + 2; 18 = 2 × 9 + 0, so the last divisor, 2, is the HCF. Check: 2 × 180 = 360 = 18 × 20.
Multiples of 18
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162 and 180. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 18?
The factors of 18 are 1, 2, 3, 6, 9 and 18. There are 6 of them.
What is the prime factorisation of 18?
18 = 2 × 3 × 3.
Is 18 a perfect square?
No. 4 × 4 = 16 and 5 × 5 = 25, and 18 lies between them.
What is the greatest factor of 18 other than itself?
9. Divide 18 by its smallest prime factor, 2, to get it.