The number 90240
90240 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 47. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 90240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90240: a Harshad number: divisible by its digit sum 15.
- 2
90240 is composite. Its prime factorisation is
- 3
The divisors add up to 293760; without 90240 itself that is 203520, so 90240 is abundant (203520 is more than 90240). Euler's totient φ(90240) = 23552 numbers up to 90240 share no factor with it.
- 4
The digits of 90240 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 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90240 = 2^{7} \times 3 \times 5 \times 47 \]90240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 293760 |
| Euler totient φ(n) | 23552 |
| Square | 8143257600 |
| Cube | 734847565824000 |
| Square root | 300.399734 (= 8√1410) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 40 |
| Scientific notation | 9.024 × |
90240 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand two hundred and forty |
| Binary (base 2) | 10110000010000000 |
| Octal (base 8) | 260200 |
| Hexadecimal (base 16) | 16080 |
| Base 3 | 11120210020 |
| As time | 90240 seconds = 25 h 4 min 0 s |
Is 90240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90240 ÷ 2 = 45120) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90240 ÷ 3 = 30080) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90240 ÷ 4 = 22560) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90240 ÷ 5 = 18048) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90240 ÷ 6 = 15040) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (90240 ÷ 8 = 11280) | 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 (90240 ÷ 10 = 9024) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90240 ÷ 12 = 7520) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90240 a prime number?
No. 90240 = × 3 × 5 × 47, so it is divisible by 2.
What are the factors of 90240?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 47, 48, 60, 64, 80, 94, 96, 120, 128, 141, 160, 188, 192, 235, 240, 282, 320, 376, 384, 470, 480, 564, 640, 705, 752, 940, 960, 1128, 1410, 1504, 1880, 1920, 2256, 2820, 3008, 3760, 4512, 5640, 6016, 7520, 9024, 11280, 15040, 18048, 22560, 30080, 45120, 90240.
What is 90240 in binary?
10110000010000000 (hexadecimal 16080, octal 260200).
What is the square root of 90240?
About 300.3997, exactly 8√1410.
Is 90240 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 90240?
90240 is a Harshad number: divisible by its digit sum 15.