FactorsAbout 240
240 has twenty factors, more than any smaller number. Four hours contain 240 minutes.
Factor pairs of 240
A factor pair is two numbers that multiply to give 240: 1 × 240, 2 × 120, 3 × 80, 4 × 60, 5 × 48, 6 × 40, 8 × 30, 10 × 24, 12 × 20 and 15 × 16. Each pair is a way of arranging 240 things in equal rows, so 240 tiles can be laid out as a rectangle in 10 different shapes.
How to find the factors of 240 by hand
Divide 240 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 15, because the next number, 16, gives 16 × 16 = 256, which is more than 240: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 240? | Result |
|---|---|---|
| 1 | yes | 1 × 240 |
| 2 | yes | 2 × 120 |
| 3 | yes | 3 × 80 |
| 4 | yes | 4 × 60 |
| 5 | yes | 5 × 48 |
| 6 | yes | 6 × 40 |
| 7 | no | remainder 2 |
| 8 | yes | 8 × 30 |
| 9 | no | remainder 6 |
| 10 | yes | 10 × 24 |
| 11 | no | remainder 9 |
| 12 | yes | 12 × 20 |
| 13 | no | remainder 6 |
| 14 | no | remainder 2 |
| 15 | yes | 15 × 16 |
The numbers that fail are 7, 9, 11, 13 and 14. All the others give a pair.
Prime factorisation of 240
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 240 = 2 × 2 × 2 × 2 × 3 × 5, which is written 24 × 3 × 5 with powers. Its prime factors are 2, 3 and 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (4 + 1) × (1 + 1) × (1 + 1) = 20. This works because a factor of 240 can use each prime anywhere from zero times up to its full power.
The 20 factors add up to 744. Leaving out 240 itself, the rest add up to 504, which is more than 240, so 240 is an abundant number. Of its factors, 4 are odd: 1, 3, 5 and 15.
Divisibility rules applied to 240
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 0, which is even.
- By 3: yes. The digits add up to 2 + 4 + 0 = 6, which is a multiple of 3.
- By 4: yes. The last two digits make 40, and 40 ÷ 4 = 10.
- By 5: yes. The last digit is 0.
- By 6: yes. A number divides by 6 when it divides by both 2 and 3. Here both tests pass.
- By 8: yes. 240 ÷ 8 = 30.
- By 9: no. The digits add up to 6, which is not a multiple of 9.
- By 10: yes. The last digit is 0.
- By 11: no. Adding alternate digits from the right gives 2 and 4. Their difference is 2, which is not 0 or a multiple of 11.
HCF and LCM with 240
240 and 225. 240 = 24 × 3 × 5 and 225 = 32 × 52. The primes they share, each with its smaller power, give the HCF: 15. Every prime with its larger power gives the LCM: 3600. By division: 240 = 225 × 1 + 15; 225 = 15 × 15 + 0, so the last divisor, 15, is the HCF. Check: 15 × 3600 = 54000 = 240 × 225.
240 and 256. 240 = 24 × 3 × 5 and 256 = 28. The primes they share, each with its smaller power, give the HCF: 16. Every prime with its larger power gives the LCM: 3840. By division: 256 = 240 × 1 + 16; 240 = 16 × 15 + 0, so the last divisor, 16, is the HCF. Check: 16 × 3840 = 61440 = 240 × 256.
Multiples of 240
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 240 are 240, 480, 720, 960, 1200, 1440, 1680, 1920, 2160 and 2400. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 240?
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240. There are 20 of them.
What is the prime factorisation of 240?
240 = 2 × 2 × 2 × 2 × 3 × 5.
Is 240 a perfect square?
No. 15 × 15 = 225 and 16 × 16 = 256, and 240 lies between them.
What is the greatest factor of 240 other than itself?
120. Divide 240 by its smallest prime factor, 2, to get it.