The number 1005
1005 is a composite number with 8 divisors. Its prime factorisation is 3 × 5 × 67. Divisors (8): 1, 3, 5, 15, 67, 201, 335, 1005.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1005 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1005 is composite. Its prime factorisation is
- 3
The divisors add up to 1632; without 1005 itself that is 627, so 1005 is deficient (627 is less than 1005). Euler's totient φ(1005) = 528 numbers up to 1005 share no factor with it.
- 4
The digits of 1005 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1005 = 3 \times 5 \times 67 \]
1005 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1632 |
| Euler totient φ(n) | 528 |
| Square | 1010025 |
| Cube | 1015075125 |
| Square root | 31.701735 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 67 |
| Scientific notation | 1.005 × |
1005 in other forms
| Form | Value |
|---|---|
| In words | one thousand and five |
| Roman numerals | MV |
| Binary (base 2) | 1111101101 |
| Octal (base 8) | 1755 |
| Hexadecimal (base 16) | 3ED |
| Base 3 | 1101020 |
| As time | 1005 seconds = 16 min 45 s |
Is 1005 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 (1005 ÷ 3 = 335) | 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 | Yes (1005 ÷ 5 = 201) | 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 4) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 4) | 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 1005 a prime number?
No. 1005 = 3 × 5 × 67, so it is divisible by 3.
What are the factors of 1005?
1, 3, 5, 15, 67, 201, 335, 1005.
What is 1005 in binary?
1111101101 (hexadecimal 3ED, octal 1755).
What is the square root of 1005?
About 31.7017.
What is 1005 in Roman numerals?
MV.
Is 1005 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 1005?
It is a composite number with 8 divisors.