The number 71984
71984 is a composite number with 20 divisors. Its prime factorisation is × 11 × 409. Divisors (20): 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 409, 818, 1636, 3272, 4499, 6544 … 71984.
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How to work it out
- 1
71984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
71984 is composite. Its prime factorisation is
- 3
The divisors add up to 152520; without 71984 itself that is 80536, so 71984 is abundant (80536 is more than 71984). Euler's totient φ(71984) = 32640 numbers up to 71984 share no factor with it.
- 4
The digits of 71984 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 71984 = 2^{4} \times 11 \times 409 \]71984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 152520 |
| Euler totient φ(n) | 32640 |
| Square | 5181696256 |
| Cube | 372999223291904 |
| Square root | 268.298341 (= 4√4499) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.1984 × |
71984 in other forms
| Form | Value |
|---|---|
| In words | seventy-one thousand nine hundred and eighty-four |
| Binary (base 2) | 10001100100110000 |
| Octal (base 8) | 214460 |
| Hexadecimal (base 16) | 11930 |
| Base 3 | 10122202002 |
| As time | 71984 seconds = 19 h 59 min 44 s |
Is 71984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (71984 ÷ 2 = 35992) | 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 (71984 ÷ 4 = 17996) | 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 3) | 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 (71984 ÷ 8 = 8998) | 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 | Yes (71984 ÷ 11 = 6544) | 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 71984 a prime number?
No. 71984 = × 11 × 409, so it is divisible by 2.
What are the factors of 71984?
1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 409, 818, 1636, 3272, 4499, 6544, 8998, 17996, 35992, 71984.
What is 71984 in binary?
10001100100110000 (hexadecimal 11930, octal 214460).
What is the square root of 71984?
About 268.2983, exactly 4√4499.
Is 71984 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 71984?
It is a composite number with 20 divisors.