The number 3360
3360 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 3360.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3360: a Harshad number: divisible by its digit sum 12.
- 2
3360 is composite. Its prime factorisation is
- 3
The divisors add up to 12096; without 3360 itself that is 8736, so 3360 is abundant (8736 is more than 3360). Euler's totient φ(3360) = 768 numbers up to 3360 share no factor with it.
- 4
The digits of 3360 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 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3360 = 2^{5} \times 3 \times 5 \times 7 \]3360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 12096 |
| Euler totient φ(n) | 768 |
| Square | 11289600 |
| Cube | 37933056000 |
| Square root | 57.965507 (= 4√210) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 43 |
| Scientific notation | 3.36 × |
3360 in other forms
| Form | Value |
|---|---|
| In words | three thousand three hundred and sixty |
| Roman numerals | MMMCCCLX |
| Binary (base 2) | 110100100000 |
| Octal (base 8) | 6440 |
| Hexadecimal (base 16) | D20 |
| Base 3 | 11121110 |
| As time | 3360 seconds = 56 min 0 s |
Is 3360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3360 ÷ 2 = 1680) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3360 ÷ 3 = 1120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3360 ÷ 4 = 840) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3360 ÷ 5 = 672) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3360 ÷ 6 = 560) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (3360 ÷ 7 = 480) | 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 (3360 ÷ 8 = 420) | 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 | Yes (3360 ÷ 10 = 336) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3360 ÷ 12 = 280) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3360 a prime number?
No. 3360 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 3360?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1120, 1680, 3360.
What is 3360 in binary?
110100100000 (hexadecimal D20, octal 6440).
What is the square root of 3360?
About 57.9655, exactly 4√210.
What is 3360 in Roman numerals?
MMMCCCLX.
Is 3360 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 3360?
3360 is a Harshad number: divisible by its digit sum 12.