The number 33008
33008 is a composite number with 10 divisors. Its prime factorisation is × 2063. Divisors (10): 1, 2, 4, 8, 16, 2063, 4126, 8252, 16504, 33008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33008: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33008 is composite. Its prime factorisation is
- 3
The divisors add up to 63984; without 33008 itself that is 30976, so 33008 is deficient (30976 is less than 33008). Euler's totient φ(33008) = 16496 numbers up to 33008 share no factor with it.
- 4
The digits of 33008 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33008 = 2^{4} \times 2063 \]33008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 63984 |
| Euler totient φ(n) | 16496 |
| Square | 1089528064 |
| Cube | 35963142336512 |
| Square root | 181.681039 (= 4√2063) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.3008 × |
33008 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and eight |
| Binary (base 2) | 1000000011110000 |
| Octal (base 8) | 100360 |
| Hexadecimal (base 16) | 80F0 |
| Base 3 | 1200021112 |
| As time | 33008 seconds = 9 h 10 min 8 s |
Is 33008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33008 ÷ 2 = 16504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33008 ÷ 4 = 8252) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (33008 ÷ 8 = 4126) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33008 a prime number?
No. 33008 = × 2063, so it is divisible by 2.
What are the factors of 33008?
1, 2, 4, 8, 16, 2063, 4126, 8252, 16504, 33008.
What is 33008 in binary?
1000000011110000 (hexadecimal 80F0, octal 100360).
What is the square root of 33008?
About 181.6810, exactly 4√2063.
Is 33008 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 33008?
33008 is a happy number: repeatedly adding the squares of its digits reaches 1.