The number 240
240 is a highly composite number: it has 20 divisors, more than any smaller number. Its prime factorisation is × 3 × 5. Divisors (20): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 240: a highly composite number: it has 20 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 6.
- 2
240 is composite. Its prime factorisation is
- 3
The divisors add up to 744; without 240 itself that is 504, so 240 is abundant (504 is more than 240). Euler's totient φ(240) = 64 numbers up to 240 share no factor with it.
- 4
The digits of 240 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 240 = 2^{4} \times 3 \times 5 \]240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 744 |
| Euler totient φ(n) | 64 |
| Square | 57600 |
| Cube | 13824000 |
| Square root | 15.491933 (= 4√15) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 21 |
| Scientific notation | 2.4 × |
240 in other forms
| Form | Value |
|---|---|
| In words | two hundred and forty |
| Roman numerals | CCXL |
| Binary (base 2) | 11110000 |
| Octal (base 8) | 360 |
| Hexadecimal (base 16) | F0 |
| Base 3 | 22220 |
| As time | 240 seconds = 4 min 0 s |
Is 240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (240 ÷ 2 = 120) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (240 ÷ 3 = 80) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (240 ÷ 4 = 60) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (240 ÷ 5 = 48) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (240 ÷ 6 = 40) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (240 ÷ 8 = 30) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (240 ÷ 10 = 24) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (240 ÷ 12 = 20) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 240 a prime number?
No. 240 = × 3 × 5, so it is divisible by 2.
What are the factors of 240?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
What is 240 in binary?
11110000 (hexadecimal F0, octal 360).
What is the square root of 240?
About 15.4919, exactly 4√15.
What is 240 in Roman numerals?
CCXL.
Is 240 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 240?
240 is a highly composite number: it has 20 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 6.