The number 4008
4008 is a composite number with 16 divisors. Its prime factorisation is × 3 × 167. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1002, 1336, 2004, 4008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4008: a Harshad number: divisible by its digit sum 12.
- 2
4008 is composite. Its prime factorisation is
- 3
The divisors add up to 10080; without 4008 itself that is 6072, so 4008 is abundant (6072 is more than 4008). Euler's totient φ(4008) = 1328 numbers up to 4008 share no factor with it.
- 4
The digits of 4008 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 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4008 = 2^{3} \times 3 \times 167 \]4008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 10080 |
| Euler totient φ(n) | 1328 |
| Square | 16064064 |
| Cube | 64384768512 |
| Square root | 63.308767 (= 2√1002) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 113 |
| Scientific notation | 4.008 × |
4008 in other forms
| Form | Value |
|---|---|
| In words | four thousand and eight |
| Binary (base 2) | 111110101000 |
| Octal (base 8) | 7650 |
| Hexadecimal (base 16) | FA8 |
| Base 3 | 12111110 |
| As time | 4008 seconds = 1 h 6 min 48 s |
Is 4008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4008 ÷ 2 = 2004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4008 ÷ 3 = 1336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4008 ÷ 4 = 1002) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (4008 ÷ 6 = 668) | 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 | Yes (4008 ÷ 8 = 501) | 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 8) | 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 | Yes (4008 ÷ 12 = 334) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4008 a prime number?
No. 4008 = × 3 × 167, so it is divisible by 2.
What are the factors of 4008?
1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1002, 1336, 2004, 4008.
What is 4008 in binary?
111110101000 (hexadecimal FA8, octal 7650).
What is the square root of 4008?
About 63.3088, exactly 2√1002.
Is 4008 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 4008?
4008 is a Harshad number: divisible by its digit sum 12.