The number 4002
4002 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 23 × 29. Divisors (16): 1, 2, 3, 6, 23, 29, 46, 58, 69, 87, 138, 174, 667, 1334, 2001, 4002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4002: a Harshad number: divisible by its digit sum 6.
- 2
4002 is composite. Its prime factorisation is
- 3
The divisors add up to 8640; without 4002 itself that is 4638, so 4002 is abundant (4638 is more than 4002). Euler's totient φ(4002) = 1232 numbers up to 4002 share no factor with it.
- 4
The digits of 4002 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 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4002 = 2 \times 3 \times 23 \times 29 \]
4002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 8640 |
| Euler totient φ(n) | 1232 |
| Square | 16016004 |
| Cube | 64096048008 |
| Square root | 63.261363 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 51 |
| Scientific notation | 4.002 × |
4002 in other forms
| Form | Value |
|---|---|
| In words | four thousand and two |
| Binary (base 2) | 111110100010 |
| Octal (base 8) | 7642 |
| Hexadecimal (base 16) | FA2 |
| Base 3 | 12111020 |
| As time | 4002 seconds = 1 h 6 min 42 s |
Is 4002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4002 ÷ 2 = 2001) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4002 ÷ 3 = 1334) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (4002 ÷ 6 = 667) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 2) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4002 a prime number?
No. 4002 = 2 × 3 × 23 × 29, so it is divisible by 2.
What are the factors of 4002?
1, 2, 3, 6, 23, 29, 46, 58, 69, 87, 138, 174, 667, 1334, 2001, 4002.
What is 4002 in binary?
111110100010 (hexadecimal FA2, octal 7642).
What is the square root of 4002?
About 63.2614.
Is 4002 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 4002?
4002 is a Harshad number: divisible by its digit sum 6.