The number 4004
4004 is a palindrome: it reads 4004 backwards too. Its prime factorisation is × 7 × 11 × 13. Divisors (24): 1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154 … 4004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4004: a palindrome: it reads 4004 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
4004 is composite. Its prime factorisation is
- 3
The divisors add up to 9408; without 4004 itself that is 5404, so 4004 is abundant (5404 is more than 4004). Euler's totient φ(4004) = 1440 numbers up to 4004 share no factor with it.
- 4
The digits of 4004 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4004 = 2^{2} \times 7 \times 11 \times 13 \]4004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 9408 |
| Euler totient φ(n) | 1440 |
| Square | 16032016 |
| Cube | 64192192064 |
| Square root | 63.277168 (= 2√1001) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 144 |
| Scientific notation | 4.004 × |
4004 in other forms
| Form | Value |
|---|---|
| In words | four thousand and four |
| Binary (base 2) | 111110100100 |
| Octal (base 8) | 7644 |
| Hexadecimal (base 16) | FA4 |
| Base 3 | 12111022 |
| As time | 4004 seconds = 1 h 6 min 44 s |
Is 4004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4004 ÷ 2 = 2002) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4004 ÷ 4 = 1001) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (4004 ÷ 7 = 572) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (4004 ÷ 11 = 364) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4004 a prime number?
No. 4004 = × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 4004?
1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002, 4004.
What is 4004 in binary?
111110100100 (hexadecimal FA4, octal 7644).
What is the square root of 4004?
About 63.2772, exactly 2√1001.
Is 4004 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 4004?
4004 is a palindrome: it reads 4004 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.