The number 1035
1035 is a triangular number: 1 + 2 + … + 45 = 1035. Its prime factorisation is × 5 × 23. Divisors (12): 1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345, 1035.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1035: a triangular number: 1 + 2 + … + 45 = 1035; a Harshad number: divisible by its digit sum 9.
- 2
1035 is composite. Its prime factorisation is
- 3
The divisors add up to 1872; without 1035 itself that is 837, so 1035 is deficient (837 is less than 1035). Euler's totient φ(1035) = 528 numbers up to 1035 share no factor with it.
- 4
The digits of 1035 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 124 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1035 = 3^{2} \times 5 \times 23 \]1035 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1872 |
| Euler totient φ(n) | 528 |
| Square | 1071225 |
| Cube | 1108717875 |
| Square root | 32.171416 (= 3√115) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 124 |
| Scientific notation | 1.035 × |
1035 in other forms
| Form | Value |
|---|---|
| In words | one thousand and thirty-five |
| Roman numerals | MXXXV |
| Binary (base 2) | 10000001011 |
| Octal (base 8) | 2013 |
| Hexadecimal (base 16) | 40B |
| Base 3 | 1102100 |
| As time | 1035 seconds = 17 min 15 s |
Is 1035 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 (1035 ÷ 3 = 345) | 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 | Yes (1035 ÷ 5 = 207) | 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 6) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1035 ÷ 9 = 115) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1035 a prime number?
No. 1035 = × 5 × 23, so it is divisible by 3.
What are the factors of 1035?
1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345, 1035.
What is 1035 in binary?
10000001011 (hexadecimal 40B, octal 2013).
What is the square root of 1035?
About 32.1714, exactly 3√115.
What is 1035 in Roman numerals?
MXXXV.
Is 1035 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1035?
1035 is a triangular number: 1 + 2 + … + 45 = 1035; a Harshad number: divisible by its digit sum 9.