The number 72015
72015 is a composite number with 8 divisors. Its prime factorisation is 3 × 5 × 4801. Divisors (8): 1, 3, 5, 15, 4801, 14403, 24005, 72015.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72015: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.
- 2
72015 is composite. Its prime factorisation is
- 3
The divisors add up to 115248; without 72015 itself that is 43233, so 72015 is deficient (43233 is less than 72015). Euler's totient φ(72015) = 38400 numbers up to 72015 share no factor with it.
- 4
The digits of 72015 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72015 = 3 \times 5 \times 4801 \]
72015 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 115248 |
| Euler totient φ(n) | 38400 |
| Square | 5186160225 |
| Cube | 373481328603375 |
| Square root | 268.356107 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 99 |
| Scientific notation | 7.2015 × |
72015 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and fifteen |
| Binary (base 2) | 10001100101001111 |
| Octal (base 8) | 214517 |
| Hexadecimal (base 16) | 1194F |
| Base 3 | 10122210020 |
| As time | 72015 seconds = 20 h 0 min 15 s |
Is 72015 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 (72015 ÷ 3 = 24005) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72015 ÷ 5 = 14403) | 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 | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72015 a prime number?
No. 72015 = 3 × 5 × 4801, so it is divisible by 3.
What are the factors of 72015?
1, 3, 5, 15, 4801, 14403, 24005, 72015.
What is 72015 in binary?
10001100101001111 (hexadecimal 1194F, octal 214517).
What is the square root of 72015?
About 268.3561.
Is 72015 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 72015?
72015 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.