The number 97984
97984 is a composite number with 14 divisors. Its prime factorisation is × 1531. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 1531, 3062, 6124, 12248, 24496, 48992, 97984.
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How to work it out
- 1
What is special about 97984: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
97984 is composite. Its prime factorisation is
- 3
The divisors add up to 194564; without 97984 itself that is 96580, so 97984 is deficient (96580 is less than 97984). Euler's totient φ(97984) = 48960 numbers up to 97984 share no factor with it.
- 4
The digits of 97984 add up to 37, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 66 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97984 = 2^{6} \times 1531 \]97984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 194564 |
| Euler totient φ(n) | 48960 |
| Square | 9600864256 |
| Cube | 940731083259904 |
| Square root | 313.023961 (= 8√1531) |
| Digit sum / digital root | 37 / 1 |
| Collatz steps to 1 | 66 |
| Scientific notation | 9.7984 × |
97984 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 10111111011000000 |
| Octal (base 8) | 277300 |
| Hexadecimal (base 16) | 17EC0 |
| Base 3 | 11222102001 |
| As time | 97984 seconds = 27 h 13 min 4 s |
Is 97984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97984 ÷ 2 = 48992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97984 ÷ 4 = 24496) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (97984 ÷ 8 = 12248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97984 a prime number?
No. 97984 = × 1531, so it is divisible by 2.
What are the factors of 97984?
1, 2, 4, 8, 16, 32, 64, 1531, 3062, 6124, 12248, 24496, 48992, 97984.
What is 97984 in binary?
10111111011000000 (hexadecimal 17EC0, octal 277300).
What is the square root of 97984?
About 313.0240, exactly 8√1531.
Is 97984 divisible by 3?
No. Its digits add up to 37, which is not a multiple of 3.
What is special about the number 97984?
97984 is a happy number: repeatedly adding the squares of its digits reaches 1.