The number 33312
33312 is a composite number with 24 divisors. Its prime factorisation is × 3 × 347. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 347, 694, 1041, 1388 … 33312.
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How to work it out
- 1
What is special about 33312: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
33312 is composite. Its prime factorisation is
- 3
The divisors add up to 87696; without 33312 itself that is 54384, so 33312 is abundant (54384 is more than 33312). Euler's totient φ(33312) = 11072 numbers up to 33312 share no factor with it.
- 4
The digits of 33312 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33312 = 2^{5} \times 3 \times 347 \]33312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 87696 |
| Euler totient φ(n) | 11072 |
| Square | 1109689344 |
| Cube | 36965971427328 |
| Square root | 182.515753 (= 4√2082) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3312 × |
33312 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand three hundred and twelve |
| Binary (base 2) | 1000001000100000 |
| Octal (base 8) | 101040 |
| Hexadecimal (base 16) | 8220 |
| Base 3 | 1200200210 |
| As time | 33312 seconds = 9 h 15 min 12 s |
Is 33312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33312 ÷ 2 = 16656) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33312 ÷ 3 = 11104) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33312 ÷ 4 = 8328) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33312 ÷ 6 = 5552) | 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 (33312 ÷ 8 = 4164) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 (33312 ÷ 12 = 2776) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33312 a prime number?
No. 33312 = × 3 × 347, so it is divisible by 2.
What are the factors of 33312?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 347, 694, 1041, 1388, 2082, 2776, 4164, 5552, 8328, 11104, 16656, 33312.
What is 33312 in binary?
1000001000100000 (hexadecimal 8220, octal 101040).
What is the square root of 33312?
About 182.5158, exactly 4√2082.
Is 33312 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 33312?
33312 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.