The number 96984
96984 is a composite number with 32 divisors. Its prime factorisation is × × 449. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 … 96984.
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How to work it out
- 1
What is special about 96984: a Harshad number: divisible by its digit sum 36.
- 2
96984 is composite. Its prime factorisation is
- 3
The divisors add up to 270000; without 96984 itself that is 173016, so 96984 is abundant (173016 is more than 96984). Euler's totient φ(96984) = 32256 numbers up to 96984 share no factor with it.
- 4
The digits of 96984 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 84 steps to reach 1.
LaTeX source of the formulas on this page
\[ 96984 = 2^{3} \times 3^{3} \times 449 \]96984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 270000 |
| Euler totient φ(n) | 32256 |
| Square | 9405896256 |
| Cube | 912221442491904 |
| Square root | 311.422543 (= 6√2694) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 84 |
| Scientific notation | 9.6984 × |
96984 in other forms
| Form | Value |
|---|---|
| In words | ninety-six thousand nine hundred and eighty-four |
| Binary (base 2) | 10111101011011000 |
| Octal (base 8) | 275330 |
| Hexadecimal (base 16) | 17AD8 |
| Base 3 | 11221001000 |
| As time | 96984 seconds = 26 h 56 min 24 s |
Is 96984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (96984 ÷ 2 = 48492) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (96984 ÷ 3 = 32328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (96984 ÷ 4 = 24246) | 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 (96984 ÷ 6 = 16164) | 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 (96984 ÷ 8 = 12123) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (96984 ÷ 9 = 10776) | 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 (96984 ÷ 12 = 8082) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 96984 a prime number?
No. 96984 = × × 449, so it is divisible by 2.
What are the factors of 96984?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 449, 898, 1347, 1796, 2694, 3592, 4041, 5388, 8082, 10776, 12123, 16164, 24246, 32328, 48492, 96984.
What is 96984 in binary?
10111101011011000 (hexadecimal 17AD8, octal 275330).
What is the square root of 96984?
About 311.4225, exactly 6√2694.
Is 96984 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 96984?
96984 is a Harshad number: divisible by its digit sum 36.