The number 30120
30120 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 251. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 30120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 30120: a Harshad number: divisible by its digit sum 6.
- 2
30120 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 30120 itself that is 60600, so 30120 is abundant (60600 is more than 30120). Euler's totient φ(30120) = 8000 numbers up to 30120 share no factor with it.
- 4
The digits of 30120 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 134 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30120 = 2^{3} \times 3 \times 5 \times 251 \]30120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 8000 |
| Square | 907214400 |
| Cube | 27325297728000 |
| Square root | 173.551145 (= 2√7530) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 134 |
| Scientific notation | 3.012 × |
30120 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand one hundred and twenty |
| Binary (base 2) | 111010110101000 |
| Octal (base 8) | 72650 |
| Hexadecimal (base 16) | 75A8 |
| Base 3 | 1112022120 |
| As time | 30120 seconds = 8 h 22 min 0 s |
Is 30120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30120 ÷ 2 = 15060) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30120 ÷ 3 = 10040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30120 ÷ 4 = 7530) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (30120 ÷ 5 = 6024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (30120 ÷ 6 = 5020) | 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 (30120 ÷ 8 = 3765) | 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 | Yes (30120 ÷ 10 = 3012) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (30120 ÷ 12 = 2510) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30120 a prime number?
No. 30120 = × 3 × 5 × 251, so it is divisible by 2.
What are the factors of 30120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 251, 502, 753, 1004, 1255, 1506, 2008, 2510, 3012, 3765, 5020, 6024, 7530, 10040, 15060, 30120.
What is 30120 in binary?
111010110101000 (hexadecimal 75A8, octal 72650).
What is the square root of 30120?
About 173.5511, exactly 2√7530.
Is 30120 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 30120?
30120 is a Harshad number: divisible by its digit sum 6.