The number 33840
33840 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 47. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 33840.
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How to work it out
- 1
What is special about 33840: a Harshad number: divisible by its digit sum 18.
- 2
33840 is composite. Its prime factorisation is
- 3
The divisors add up to 116064; without 33840 itself that is 82224, so 33840 is abundant (82224 is more than 33840). Euler's totient φ(33840) = 8832 numbers up to 33840 share no factor with it.
- 4
The digits of 33840 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33840 = 2^{4} \times 3^{2} \times 5 \times 47 \]33840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 116064 |
| Euler totient φ(n) | 8832 |
| Square | 1145145600 |
| Cube | 38751727104000 |
| Square root | 183.956517 (= 12√235) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.384 × |
33840 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and forty |
| Binary (base 2) | 1000010000110000 |
| Octal (base 8) | 102060 |
| Hexadecimal (base 16) | 8430 |
| Base 3 | 1201102100 |
| As time | 33840 seconds = 9 h 24 min 0 s |
Is 33840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33840 ÷ 2 = 16920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33840 ÷ 3 = 11280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33840 ÷ 4 = 8460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33840 ÷ 5 = 6768) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33840 ÷ 6 = 5640) | 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 (33840 ÷ 8 = 4230) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33840 ÷ 9 = 3760) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33840 ÷ 10 = 3384) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33840 ÷ 12 = 2820) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33840 a prime number?
No. 33840 = × × 5 × 47, so it is divisible by 2.
What are the factors of 33840?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 47, 48, 60, 72, 80, 90, 94, 120, 141, 144, 180, 188, 235, 240, 282, 360, 376, 423, 470, 564, 705, 720, 752, 846, 940, 1128, 1410, 1692, 1880, 2115, 2256, 2820, 3384, 3760, 4230, 5640, 6768, 8460, 11280, 16920, 33840.
What is 33840 in binary?
1000010000110000 (hexadecimal 8430, octal 102060).
What is the square root of 33840?
About 183.9565, exactly 12√235.
Is 33840 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33840?
33840 is a Harshad number: divisible by its digit sum 18.