The number 3456
3456 is a composite number with 32 divisors. Its prime factorisation is × . Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 3456.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3456: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
3456 is composite. Its prime factorisation is
- 3
The divisors add up to 10200; without 3456 itself that is 6744, so 3456 is abundant (6744 is more than 3456). Euler's totient φ(3456) = 1152 numbers up to 3456 share no factor with it.
- 4
The digits of 3456 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3456 = 2^{7} \times 3^{3} \]3456 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 10200 |
| Euler totient φ(n) | 1152 |
| Square | 11943936 |
| Cube | 41278242816 |
| Square root | 58.787754 (= 24√6) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 118 |
| Scientific notation | 3.456 × |
3456 in other forms
| Form | Value |
|---|---|
| In words | three thousand four hundred and fifty-six |
| Roman numerals | MMMCDLVI |
| Binary (base 2) | 110110000000 |
| Octal (base 8) | 6600 |
| Hexadecimal (base 16) | D80 |
| Base 3 | 11202000 |
| As time | 3456 seconds = 57 min 36 s |
Is 3456 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3456 ÷ 2 = 1728) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3456 ÷ 3 = 1152) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3456 ÷ 4 = 864) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3456 ÷ 6 = 576) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (3456 ÷ 8 = 432) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3456 ÷ 9 = 384) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3456 ÷ 12 = 288) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3456 a prime number?
No. 3456 = × , so it is divisible by 2.
What are the factors of 3456?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728, 3456.
What is 3456 in binary?
110110000000 (hexadecimal D80, octal 6600).
What is the square root of 3456?
About 58.7878, exactly 24√6.
What is 3456 in Roman numerals?
MMMCDLVI.
Is 3456 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3456?
3456 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.