The number 72009
72009 is a composite number with 20 divisors. Its prime factorisation is × 7 × 127. Divisors (20): 1, 3, 7, 9, 21, 27, 63, 81, 127, 189, 381, 567, 889, 1143, 2667, 3429 … 72009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72009 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72009 is composite. Its prime factorisation is
- 3
The divisors add up to 123904; without 72009 itself that is 51895, so 72009 is deficient (51895 is less than 72009). Euler's totient φ(72009) = 40824 numbers up to 72009 share no factor with it.
- 4
The digits of 72009 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72009 = 3^{4} \times 7 \times 127 \]72009 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 123904 |
| Euler totient φ(n) | 40824 |
| Square | 5185296081 |
| Cube | 373387985496729 |
| Square root | 268.344927 (= 9√889) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2009 × |
72009 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and nine |
| Binary (base 2) | 10001100101001001 |
| Octal (base 8) | 214511 |
| Hexadecimal (base 16) | 11949 |
| Base 3 | 10122210000 |
| As time | 72009 seconds = 20 h 0 min 9 s |
Is 72009 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 | Yes (72009 ÷ 3 = 24003) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72009 ÷ 7 = 10287) | 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 | Yes (72009 ÷ 9 = 8001) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72009 a prime number?
No. 72009 = × 7 × 127, so it is divisible by 3.
What are the factors of 72009?
1, 3, 7, 9, 21, 27, 63, 81, 127, 189, 381, 567, 889, 1143, 2667, 3429, 8001, 10287, 24003, 72009.
What is 72009 in binary?
10001100101001001 (hexadecimal 11949, octal 214511).
What is the square root of 72009?
About 268.3449, exactly 9√889.
Is 72009 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72009?
It is a composite number with 20 divisors.