The number 5000
5000 is a composite number with 20 divisors. Its prime factorisation is × . Divisors (20): 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625 … 5000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5000: a Harshad number: divisible by its digit sum 5.
- 2
5000 is composite. Its prime factorisation is
- 3
The divisors add up to 11715; without 5000 itself that is 6715, so 5000 is abundant (6715 is more than 5000). Euler's totient φ(5000) = 2000 numbers up to 5000 share no factor with it.
- 4
The digits of 5000 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5000 = 2^{3} \times 5^{4} \]5000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 11715 |
| Euler totient φ(n) | 2000 |
| Square | 25000000 |
| Cube | 125000000000 |
| Square root | 70.710678 (= 50√2) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 28 |
| Scientific notation | 5 × |
5000 in other forms
| Form | Value |
|---|---|
| In words | five thousand |
| Binary (base 2) | 1001110001000 |
| Octal (base 8) | 11610 |
| Hexadecimal (base 16) | 1388 |
| Base 3 | 20212012 |
| As time | 5000 seconds = 1 h 23 min 20 s |
Is 5000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5000 ÷ 2 = 2500) | 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 (5000 ÷ 4 = 1250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5000 ÷ 5 = 1000) | 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 | No (remainder 2) | 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 (5000 ÷ 8 = 625) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5000 ÷ 10 = 500) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 5000 a prime number?
No. 5000 = × , so it is divisible by 2.
What are the factors of 5000?
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000.
What is 5000 in binary?
1001110001000 (hexadecimal 1388, octal 11610).
What is the square root of 5000?
About 70.7107, exactly 50√2.
Is 5000 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 5000?
5000 is a Harshad number: divisible by its digit sum 5.