The number 9120
9120 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 19. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32 … 9120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
9120 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 9120 itself that is 21120, so 9120 is abundant (21120 is more than 9120). Euler's totient φ(9120) = 2304 numbers up to 9120 share no factor with it.
- 4
The digits of 9120 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 109 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9120 = 2^{5} \times 3 \times 5 \times 19 \]9120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 2304 |
| Square | 83174400 |
| Cube | 758550528000 |
| Square root | 95.498691 (= 4√570) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 109 |
| Scientific notation | 9.12 × |
9120 in other forms
| Form | Value |
|---|---|
| In words | nine thousand one hundred and twenty |
| Binary (base 2) | 10001110100000 |
| Octal (base 8) | 21640 |
| Hexadecimal (base 16) | 23A0 |
| Base 3 | 110111210 |
| As time | 9120 seconds = 2 h 32 min 0 s |
Is 9120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9120 ÷ 2 = 4560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9120 ÷ 3 = 3040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9120 ÷ 4 = 2280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9120 ÷ 5 = 1824) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9120 ÷ 6 = 1520) | 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 (9120 ÷ 8 = 1140) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9120 ÷ 10 = 912) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9120 ÷ 12 = 760) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9120 a prime number?
No. 9120 = × 3 × 5 × 19, so it is divisible by 2.
What are the factors of 9120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120.
What is 9120 in binary?
10001110100000 (hexadecimal 23A0, octal 21640).
What is the square root of 9120?
About 95.4987, exactly 4√570.
Is 9120 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 9120?
9120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.