The number 73984
73984 is a perfect square (272²). Its prime factorisation is × . Divisors (27): 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 289, 544 … 73984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73984: a perfect square (272²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
73984 is composite. Its prime factorisation is
- 3
The divisors add up to 156877; without 73984 itself that is 82893, so 73984 is abundant (82893 is more than 73984). Euler's totient φ(73984) = 34816 numbers up to 73984 share no factor with it.
- 4
The digits of 73984 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73984 = 2^{8} \times 17^{2} \]73984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 156877 |
| Euler totient φ(n) | 34816 |
| Square | 5473632256 |
| Cube | 404961208827904 |
| Square root | 272 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 37 |
| Scientific notation | 7.3984 × |
| Perfect power |
73984 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand nine hundred and eighty-four |
| Binary (base 2) | 10010000100000000 |
| Octal (base 8) | 220400 |
| Hexadecimal (base 16) | 12100 |
| Base 3 | 10202111011 |
| As time | 73984 seconds = 20 h 33 min 4 s |
Is 73984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73984 ÷ 2 = 36992) | 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 (73984 ÷ 4 = 18496) | 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 1) | 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 (73984 ÷ 8 = 9248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 9) | 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 73984 a prime number?
No. 73984 = × , so it is divisible by 2.
What are the factors of 73984?
1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 289, 544, 578, 1088, 1156, 2176, 2312, 4352, 4624, 9248, 18496, 36992, 73984.
What is 73984 in binary?
10010000100000000 (hexadecimal 12100, octal 220400).
What is the square root of 73984?
272, because 272 × 272 = 73984.
Is 73984 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 73984?
73984 is a perfect square (272²); a happy number: repeatedly adding the squares of its digits reaches 1.