The number 561
561 is a triangular number: 1 + 2 + … + 33 = 561 and a binary palindrome (1000110001). Its prime factorisation is 3 × 11 × 17. Divisors (8): 1, 3, 11, 17, 33, 51, 187, 561.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 561: a triangular number: 1 + 2 + … + 33 = 561; a binary palindrome (1000110001).
- 2
561 is composite. Its prime factorisation is
- 3
The divisors add up to 864; without 561 itself that is 303, so 561 is deficient (303 is less than 561). Euler's totient φ(561) = 320 numbers up to 561 share no factor with it.
- 4
The digits of 561 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
\[ 561 = 3 \times 11 \times 17 \]
561 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 864 |
| Euler totient φ(n) | 320 |
| Square | 314721 |
| Cube | 176558481 |
| Square root | 23.685439 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 43 |
| Scientific notation | 5.61 × |
561 in other forms
| Form | Value |
|---|---|
| In words | five hundred and sixty-one |
| Roman numerals | DLXI |
| Binary (base 2) | 1000110001 |
| Octal (base 8) | 1061 |
| Hexadecimal (base 16) | 231 |
| Base 3 | 202210 |
| As time | 561 seconds = 9 min 21 s |
Is 561 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (561 ÷ 3 = 187) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | 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 | No (remainder 1) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (561 ÷ 11 = 51) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 561 a prime number?
No. 561 = 3 × 11 × 17, so it is divisible by 3.
What are the factors of 561?
1, 3, 11, 17, 33, 51, 187, 561.
What is 561 in binary?
1000110001 (hexadecimal 231, octal 1061).
What is the square root of 561?
About 23.6854.
What is 561 in Roman numerals?
DLXI.
Is 561 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 561?
561 is a triangular number: 1 + 2 + … + 33 = 561; a binary palindrome (1000110001).