The number 4005
4005 is a triangular number: 1 + 2 + … + 89 = 4005. Its prime factorisation is × 5 × 89. Divisors (12): 1, 3, 5, 9, 15, 45, 89, 267, 445, 801, 1335, 4005.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4005: a triangular number: 1 + 2 + … + 89 = 4005; a Harshad number: divisible by its digit sum 9.
- 2
4005 is composite. Its prime factorisation is
- 3
The divisors add up to 7020; without 4005 itself that is 3015, so 4005 is deficient (3015 is less than 4005). Euler's totient φ(4005) = 2112 numbers up to 4005 share no factor with it.
- 4
The digits of 4005 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 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4005 = 3^{2} \times 5 \times 89 \]4005 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 7020 |
| Euler totient φ(n) | 2112 |
| Square | 16040025 |
| Cube | 64240300125 |
| Square root | 63.285069 (= 3√445) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 144 |
| Scientific notation | 4.005 × |
4005 in other forms
| Form | Value |
|---|---|
| In words | four thousand and five |
| Binary (base 2) | 111110100101 |
| Octal (base 8) | 7645 |
| Hexadecimal (base 16) | FA5 |
| Base 3 | 12111100 |
| As time | 4005 seconds = 1 h 6 min 45 s |
Is 4005 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 (4005 ÷ 3 = 1335) | 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 (4005 ÷ 5 = 801) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (4005 ÷ 9 = 445) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4005 a prime number?
No. 4005 = × 5 × 89, so it is divisible by 3.
What are the factors of 4005?
1, 3, 5, 9, 15, 45, 89, 267, 445, 801, 1335, 4005.
What is 4005 in binary?
111110100101 (hexadecimal FA5, octal 7645).
What is the square root of 4005?
About 63.2851, exactly 3√445.
Is 4005 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 4005?
4005 is a triangular number: 1 + 2 + … + 89 = 4005; a Harshad number: divisible by its digit sum 9.