The number 89984
89984 is a composite number with 32 divisors. Its prime factorisation is × 19 × 37. Divisors (32): 1, 2, 4, 8, 16, 19, 32, 37, 38, 64, 74, 76, 128, 148, 152, 296 … 89984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 89984: a Harshad number: divisible by its digit sum 38.
- 2
89984 is composite. Its prime factorisation is
- 3
The divisors add up to 193800; without 89984 itself that is 103816, so 89984 is abundant (103816 is more than 89984). Euler's totient φ(89984) = 41472 numbers up to 89984 share no factor with it.
- 4
The digits of 89984 add up to 38, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 177 steps to reach 1.
LaTeX source of the formulas on this page
\[ 89984 = 2^{7} \times 19 \times 37 \]89984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 193800 |
| Euler totient φ(n) | 41472 |
| Square | 8097120256 |
| Cube | 728611269115904 |
| Square root | 299.973332 (= 8√1406) |
| Digit sum / digital root | 38 / 2 |
| Collatz steps to 1 | 177 |
| Scientific notation | 8.9984 × |
89984 in other forms
| Form | Value |
|---|---|
| In words | eighty-nine thousand nine hundred and eighty-four |
| Binary (base 2) | 10101111110000000 |
| Octal (base 8) | 257600 |
| Hexadecimal (base 16) | 15F80 |
| Base 3 | 11120102202 |
| As time | 89984 seconds = 24 h 59 min 44 s |
Is 89984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (89984 ÷ 2 = 44992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (89984 ÷ 4 = 22496) | 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 | No (remainder 2) | 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 (89984 ÷ 8 = 11248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 89984 a prime number?
No. 89984 = × 19 × 37, so it is divisible by 2.
What are the factors of 89984?
1, 2, 4, 8, 16, 19, 32, 37, 38, 64, 74, 76, 128, 148, 152, 296, 304, 592, 608, 703, 1184, 1216, 1406, 2368, 2432, 2812, 4736, 5624, 11248, 22496, 44992, 89984.
What is 89984 in binary?
10101111110000000 (hexadecimal 15F80, octal 257600).
What is the square root of 89984?
About 299.9733, exactly 8√1406.
Is 89984 divisible by 3?
No. Its digits add up to 38, which is not a multiple of 3.
What is special about the number 89984?
89984 is a Harshad number: divisible by its digit sum 38.