The number 1000
1000 is a perfect cube (). Its prime factorisation is × . Divisors (16): 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1000: a perfect cube (); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.
- 2
1000 is composite. Its prime factorisation is
- 3
The divisors add up to 2340; without 1000 itself that is 1340, so 1000 is abundant (1340 is more than 1000). Euler's totient φ(1000) = 400 numbers up to 1000 share no factor with it.
- 4
The digits of 1000 add up to 1, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1000 = 2^{3} \times 5^{3} \]1000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2340 |
| Euler totient φ(n) | 400 |
| Square | 1000000 |
| Cube | 1000000000 |
| Square root | 31.622777 (= 10√10) |
| Digit sum / digital root | 1 / 1 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1 × |
| Perfect power |
1000 in other forms
| Form | Value |
|---|---|
| In words | one thousand |
| Roman numerals | M |
| Binary (base 2) | 1111101000 |
| Octal (base 8) | 1750 |
| Hexadecimal (base 16) | 3E8 |
| Base 3 | 1101001 |
| As time | 1000 seconds = 16 min 40 s |
Is 1000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1000 ÷ 2 = 500) | 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 (1000 ÷ 4 = 250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1000 ÷ 5 = 200) | 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 6) | 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 (1000 ÷ 8 = 125) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1000 ÷ 10 = 100) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 1000 a prime number?
No. 1000 = × , so it is divisible by 2.
What are the factors of 1000?
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
What is 1000 in binary?
1111101000 (hexadecimal 3E8, octal 1750).
What is the square root of 1000?
About 31.6228, exactly 10√10.
What is 1000 in Roman numerals?
M.
Is 1000 divisible by 3?
No. Its digits add up to 1, which is not a multiple of 3.
What is special about the number 1000?
1000 is a perfect cube (); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.