The number 4000
4000 is a composite number with 24 divisors. Its prime factorisation is × . Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160 … 4000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4000: a Harshad number: divisible by its digit sum 4.
- 2
4000 is composite. Its prime factorisation is
- 3
The divisors add up to 9828; without 4000 itself that is 5828, so 4000 is abundant (5828 is more than 4000). Euler's totient φ(4000) = 1600 numbers up to 4000 share no factor with it.
- 4
The digits of 4000 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4000 = 2^{5} \times 5^{3} \]4000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 9828 |
| Euler totient φ(n) | 1600 |
| Square | 16000000 |
| Cube | 64000000000 |
| Square root | 63.245553 (= 20√10) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 113 |
| Scientific notation | 4 × |
4000 in other forms
| Form | Value |
|---|---|
| In words | four thousand |
| Binary (base 2) | 111110100000 |
| Octal (base 8) | 7640 |
| Hexadecimal (base 16) | FA0 |
| Base 3 | 12111011 |
| As time | 4000 seconds = 1 h 6 min 40 s |
Is 4000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4000 ÷ 2 = 2000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4000 ÷ 4 = 1000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4000 ÷ 5 = 800) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (4000 ÷ 8 = 500) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4000 ÷ 10 = 400) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4000 a prime number?
No. 4000 = × , so it is divisible by 2.
What are the factors of 4000?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.
What is 4000 in binary?
111110100000 (hexadecimal FA0, octal 7640).
What is the square root of 4000?
About 63.2456, exactly 20√10.
Is 4000 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 4000?
4000 is a Harshad number: divisible by its digit sum 4.