The number 3312
3312 is a composite number with 30 divisors. Its prime factorisation is × × 23. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69 … 3312.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3312: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
3312 is composite. Its prime factorisation is
- 3
The divisors add up to 9672; without 3312 itself that is 6360, so 3312 is abundant (6360 is more than 3312). Euler's totient φ(3312) = 1056 numbers up to 3312 share no factor with it.
- 4
The digits of 3312 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3312 = 2^{4} \times 3^{2} \times 23 \]3312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 9672 |
| Euler totient φ(n) | 1056 |
| Square | 10969344 |
| Cube | 36330467328 |
| Square root | 57.549978 (= 12√23) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 92 |
| Scientific notation | 3.312 × |
3312 in other forms
| Form | Value |
|---|---|
| In words | three thousand three hundred and twelve |
| Roman numerals | MMMCCCXII |
| Binary (base 2) | 110011110000 |
| Octal (base 8) | 6360 |
| Hexadecimal (base 16) | CF0 |
| Base 3 | 11112200 |
| As time | 3312 seconds = 55 min 12 s |
Is 3312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3312 ÷ 2 = 1656) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3312 ÷ 3 = 1104) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3312 ÷ 4 = 828) | 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 (3312 ÷ 6 = 552) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (3312 ÷ 8 = 414) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3312 ÷ 9 = 368) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3312 ÷ 12 = 276) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3312 a prime number?
No. 3312 = × × 23, so it is divisible by 2.
What are the factors of 3312?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 552, 828, 1104, 1656, 3312.
What is 3312 in binary?
110011110000 (hexadecimal CF0, octal 6360).
What is the square root of 3312?
About 57.5500, exactly 12√23.
What is 3312 in Roman numerals?
MMMCCCXII.
Is 3312 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3312?
3312 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.