The number 1071
1071 is a composite number with 12 divisors. Its prime factorisation is × 7 × 17. Divisors (12): 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1071: a Harshad number: divisible by its digit sum 9.
- 2
1071 is composite. Its prime factorisation is
- 3
The divisors add up to 1872; without 1071 itself that is 801, so 1071 is deficient (801 is less than 1071). Euler's totient φ(1071) = 576 numbers up to 1071 share no factor with it.
- 4
The digits of 1071 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 168 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1071 = 3^{2} \times 7 \times 17 \]1071 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1872 |
| Euler totient φ(n) | 576 |
| Square | 1147041 |
| Cube | 1228480911 |
| Square root | 32.726136 (= 3√119) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 168 |
| Scientific notation | 1.071 × |
1071 in other forms
| Form | Value |
|---|---|
| In words | one thousand and seventy-one |
| Roman numerals | MLXXI |
| Binary (base 2) | 10000101111 |
| Octal (base 8) | 2057 |
| Hexadecimal (base 16) | 42F |
| Base 3 | 1110200 |
| As time | 1071 seconds = 17 min 51 s |
Is 1071 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 (1071 ÷ 3 = 357) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | Yes (1071 ÷ 7 = 153) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1071 ÷ 9 = 119) | 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 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1071 a prime number?
No. 1071 = × 7 × 17, so it is divisible by 3.
What are the factors of 1071?
1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
What is 1071 in binary?
10000101111 (hexadecimal 42F, octal 2057).
What is the square root of 1071?
About 32.7261, exactly 3√119.
What is 1071 in Roman numerals?
MLXXI.
Is 1071 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1071?
1071 is a Harshad number: divisible by its digit sum 9.