The number 1009
1009 is the 169th prime number. Its only divisors are 1 and 1009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1009: the 169th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1009 is prime, so its only factors are 1 and 1009. It is the 169th prime; the next prime is 1013 and the one before is 997.
- 3
The divisors add up to 1010; without 1009 itself that is 1, so 1009 is deficient (1 is less than 1009). Euler's totient φ(1009) = 1008 numbers up to 1009 share no factor with it.
- 4
The digits of 1009 add up to 10, 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.
1009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1010 |
| Euler totient φ(n) | 1008 |
| Square | 1018081 |
| Cube | 1027243729 |
| Square root | 31.764760 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1.009 × |
1009 in other forms
| Form | Value |
|---|---|
| In words | one thousand and nine |
| Roman numerals | MIX |
| Binary (base 2) | 1111110001 |
| Octal (base 8) | 1761 |
| Hexadecimal (base 16) | 3F1 |
| Base 3 | 1101101 |
| As time | 1009 seconds = 16 min 49 s |
Is 1009 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 1) | 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 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1009 a prime number?
Yes. 1009 is divisible only by 1 and itself.
What are the factors of 1009?
1, 1009.
What is 1009 in binary?
1111110001 (hexadecimal 3F1, octal 1761).
What is the square root of 1009?
About 31.7648.
What is 1009 in Roman numerals?
MIX.
Is 1009 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1009?
1009 is the 169th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.