The number 30984
30984 is a composite number with 16 divisors. Its prime factorisation is × 3 × 1291. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492, 30984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 30984: a Harshad number: divisible by its digit sum 24.
- 2
30984 is composite. Its prime factorisation is
- 3
The divisors add up to 77520; without 30984 itself that is 46536, so 30984 is abundant (46536 is more than 30984). Euler's totient φ(30984) = 10320 numbers up to 30984 share no factor with it.
- 4
The digits of 30984 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30984 = 2^{3} \times 3 \times 1291 \]30984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 77520 |
| Euler totient φ(n) | 10320 |
| Square | 960008256 |
| Cube | 29744895803904 |
| Square root | 176.022726 (= 2√7746) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.0984 × |
30984 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand nine hundred and eighty-four |
| Binary (base 2) | 111100100001000 |
| Octal (base 8) | 74410 |
| Hexadecimal (base 16) | 7908 |
| Base 3 | 1120111120 |
| As time | 30984 seconds = 8 h 36 min 24 s |
Is 30984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30984 ÷ 2 = 15492) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30984 ÷ 3 = 10328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30984 ÷ 4 = 7746) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (30984 ÷ 6 = 5164) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (30984 ÷ 8 = 3873) | 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 4) | 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 (30984 ÷ 12 = 2582) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30984 a prime number?
No. 30984 = × 3 × 1291, so it is divisible by 2.
What are the factors of 30984?
1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492, 30984.
What is 30984 in binary?
111100100001000 (hexadecimal 7908, octal 74410).
What is the square root of 30984?
About 176.0227, exactly 2√7746.
Is 30984 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 30984?
30984 is a Harshad number: divisible by its digit sum 24.