The number 33760
33760 is a composite number with 24 divisors. Its prime factorisation is × 5 × 211. Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 211, 422, 844, 1055 … 33760.
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How to work it out
- 1
What is special about 33760: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33760 is composite. Its prime factorisation is
- 3
The divisors add up to 80136; without 33760 itself that is 46376, so 33760 is abundant (46376 is more than 33760). Euler's totient φ(33760) = 13440 numbers up to 33760 share no factor with it.
- 4
The digits of 33760 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 173 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33760 = 2^{5} \times 5 \times 211 \]33760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 80136 |
| Euler totient φ(n) | 13440 |
| Square | 1139737600 |
| Cube | 38477541376000 |
| Square root | 183.738945 (= 4√2110) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 173 |
| Scientific notation | 3.376 × |
33760 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand seven hundred and sixty |
| Binary (base 2) | 1000001111100000 |
| Octal (base 8) | 101740 |
| Hexadecimal (base 16) | 83E0 |
| Base 3 | 1201022101 |
| As time | 33760 seconds = 9 h 22 min 40 s |
Is 33760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33760 ÷ 2 = 16880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33760 ÷ 4 = 8440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33760 ÷ 5 = 6752) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (33760 ÷ 8 = 4220) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33760 ÷ 10 = 3376) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33760 a prime number?
No. 33760 = × 5 × 211, so it is divisible by 2.
What are the factors of 33760?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 211, 422, 844, 1055, 1688, 2110, 3376, 4220, 6752, 8440, 16880, 33760.
What is 33760 in binary?
1000001111100000 (hexadecimal 83E0, octal 101740).
What is the square root of 33760?
About 183.7389, exactly 4√2110.
Is 33760 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 33760?
33760 is a happy number: repeatedly adding the squares of its digits reaches 1.