The number 9072
9072 is a composite number with 50 divisors. Its prime factorisation is × × 7. Divisors (50): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 9072.
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How to work it out
- 1
What is special about 9072: a Harshad number: divisible by its digit sum 18.
- 2
9072 is composite. Its prime factorisation is
- 3
The divisors add up to 30008; without 9072 itself that is 20936, so 9072 is abundant (20936 is more than 9072). Euler's totient φ(9072) = 2592 numbers up to 9072 share no factor with it.
- 4
The digits of 9072 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 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9072 = 2^{4} \times 3^{4} \times 7 \]9072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 50 |
| Sum of divisors | 30008 |
| Euler totient φ(n) | 2592 |
| Square | 82301184 |
| Cube | 746636341248 |
| Square root | 95.247047 (= 36√7) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 65 |
| Scientific notation | 9.072 × |
9072 in other forms
| Form | Value |
|---|---|
| In words | nine thousand and seventy-two |
| Binary (base 2) | 10001101110000 |
| Octal (base 8) | 21560 |
| Hexadecimal (base 16) | 2370 |
| Base 3 | 110110000 |
| As time | 9072 seconds = 2 h 31 min 12 s |
Is 9072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9072 ÷ 2 = 4536) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9072 ÷ 3 = 3024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9072 ÷ 4 = 2268) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9072 ÷ 6 = 1512) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9072 ÷ 7 = 1296) | 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 (9072 ÷ 8 = 1134) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9072 ÷ 9 = 1008) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | Yes (9072 ÷ 12 = 756) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9072 a prime number?
No. 9072 = × × 7, so it is divisible by 2.
What are the factors of 9072?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 252, 324, 336, 378, 432, 504, 567, 648, 756, 1008, 1134, 1296, 1512, 2268, 3024, 4536, 9072.
What is 9072 in binary?
10001101110000 (hexadecimal 2370, octal 21560).
What is the square root of 9072?
About 95.2470, exactly 36√7.
Is 9072 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9072?
9072 is a Harshad number: divisible by its digit sum 18.