The number 33880
33880 is a composite number with 48 divisors. Its prime factorisation is × 5 × 7 × . Divisors (48): 1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 28, 35, 40, 44, 55 … 33880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33880: a Harshad number: divisible by its digit sum 22.
- 2
33880 is composite. Its prime factorisation is
- 3
The divisors add up to 95760; without 33880 itself that is 61880, so 33880 is abundant (61880 is more than 33880). Euler's totient φ(33880) = 10560 numbers up to 33880 share no factor with it.
- 4
The digits of 33880 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33880 = 2^{3} \times 5 \times 7 \times 11^{2} \]33880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 95760 |
| Euler totient φ(n) | 10560 |
| Square | 1147854400 |
| Cube | 38889307072000 |
| Square root | 184.065206 (= 22√70) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 59 |
| Scientific notation | 3.388 × |
33880 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and eighty |
| Binary (base 2) | 1000010001011000 |
| Octal (base 8) | 102130 |
| Hexadecimal (base 16) | 8458 |
| Base 3 | 1201110211 |
| As time | 33880 seconds = 9 h 24 min 40 s |
Is 33880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33880 ÷ 2 = 16940) | 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 (33880 ÷ 4 = 8470) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33880 ÷ 5 = 6776) | 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 | Yes (33880 ÷ 7 = 4840) | 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 (33880 ÷ 8 = 4235) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33880 ÷ 10 = 3388) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (33880 ÷ 11 = 3080) | 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 33880 a prime number?
No. 33880 = × 5 × 7 × , so it is divisible by 2.
What are the factors of 33880?
1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 88, 110, 121, 140, 154, 220, 242, 280, 308, 385, 440, 484, 605, 616, 770, 847, 968, 1210, 1540, 1694, 2420, 3080, 3388, 4235, 4840, 6776, 8470, 16940, 33880.
What is 33880 in binary?
1000010001011000 (hexadecimal 8458, octal 102130).
What is the square root of 33880?
About 184.0652, exactly 22√70.
Is 33880 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 33880?
33880 is a Harshad number: divisible by its digit sum 22.