The number 9240
9240 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 7 × 11. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22 … 9240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9240: a Harshad number: divisible by its digit sum 15.
- 2
9240 is composite. Its prime factorisation is
- 3
The divisors add up to 34560; without 9240 itself that is 25320, so 9240 is abundant (25320 is more than 9240). Euler's totient φ(9240) = 1920 numbers up to 9240 share no factor with it.
- 4
The digits of 9240 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9240 = 2^{3} \times 3 \times 5 \times 7 \times 11 \]9240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 34560 |
| Euler totient φ(n) | 1920 |
| Square | 85377600 |
| Cube | 788889024000 |
| Square root | 96.124919 (= 2√2310) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 34 |
| Scientific notation | 9.24 × |
9240 in other forms
| Form | Value |
|---|---|
| In words | nine thousand two hundred and forty |
| Binary (base 2) | 10010000011000 |
| Octal (base 8) | 22030 |
| Hexadecimal (base 16) | 2418 |
| Base 3 | 110200020 |
| As time | 9240 seconds = 2 h 34 min 0 s |
Is 9240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9240 ÷ 2 = 4620) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9240 ÷ 3 = 3080) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9240 ÷ 4 = 2310) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9240 ÷ 5 = 1848) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9240 ÷ 6 = 1540) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9240 ÷ 7 = 1320) | 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 (9240 ÷ 8 = 1155) | 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 (9240 ÷ 10 = 924) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9240 ÷ 11 = 840) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9240 ÷ 12 = 770) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9240 a prime number?
No. 9240 = × 3 × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 9240?
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 28, 30, 33, 35, 40, 42, 44, 55, 56, 60, 66, 70, 77, 84, 88, 105, 110, 120, 132, 140, 154, 165, 168, 210, 220, 231, 264, 280, 308, 330, 385, 420, 440, 462, 616, 660, 770, 840, 924, 1155, 1320, 1540, 1848, 2310, 3080, 4620, 9240.
What is 9240 in binary?
10010000011000 (hexadecimal 2418, octal 22030).
What is the square root of 9240?
About 96.1249, exactly 2√2310.
Is 9240 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 9240?
9240 is a Harshad number: divisible by its digit sum 15.