The number 30720
30720 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 30720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 30720: a Harshad number: divisible by its digit sum 12.
- 2
30720 is composite. Its prime factorisation is
- 3
The divisors add up to 98280; without 30720 itself that is 67560, so 30720 is abundant (67560 is more than 30720). Euler's totient φ(30720) = 8192 numbers up to 30720 share no factor with it.
- 4
The digits of 30720 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 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30720 = 2^{11} \times 3 \times 5 \]30720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 98280 |
| Euler totient φ(n) | 8192 |
| Square | 943718400 |
| Cube | 28991029248000 |
| Square root | 175.271218 (= 32√30) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 28 |
| Scientific notation | 3.072 × |
30720 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand seven hundred and twenty |
| Binary (base 2) | 111100000000000 |
| Octal (base 8) | 74000 |
| Hexadecimal (base 16) | 7800 |
| Base 3 | 1120010210 |
| As time | 30720 seconds = 8 h 32 min 0 s |
Is 30720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30720 ÷ 2 = 15360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30720 ÷ 3 = 10240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30720 ÷ 4 = 7680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (30720 ÷ 5 = 6144) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (30720 ÷ 6 = 5120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (30720 ÷ 8 = 3840) | 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 (30720 ÷ 10 = 3072) | 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 (30720 ÷ 12 = 2560) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30720 a prime number?
No. 30720 = × 3 × 5, so it is divisible by 2.
What are the factors of 30720?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 5120, 6144, 7680, 10240, 15360, 30720.
What is 30720 in binary?
111100000000000 (hexadecimal 7800, octal 74000).
What is the square root of 30720?
About 175.2712, exactly 32√30.
Is 30720 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 30720?
30720 is a Harshad number: divisible by its digit sum 12.