The number 75984
75984 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1583. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1583, 3166, 4749, 6332, 9498, 12664 … 75984.
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How to work it out
- 1
75984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
75984 is composite. Its prime factorisation is
- 3
The divisors add up to 196416; without 75984 itself that is 120432, so 75984 is abundant (120432 is more than 75984). Euler's totient φ(75984) = 25312 numbers up to 75984 share no factor with it.
- 4
The digits of 75984 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 81 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75984 = 2^{4} \times 3 \times 1583 \]75984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 196416 |
| Euler totient φ(n) | 25312 |
| Square | 5773568256 |
| Cube | 438698810363904 |
| Square root | 275.651954 (= 4√4749) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 81 |
| Scientific notation | 7.5984 × |
75984 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand nine hundred and eighty-four |
| Binary (base 2) | 10010100011010000 |
| Octal (base 8) | 224320 |
| Hexadecimal (base 16) | 128D0 |
| Base 3 | 10212020020 |
| As time | 75984 seconds = 21 h 6 min 24 s |
Is 75984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75984 ÷ 2 = 37992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75984 ÷ 3 = 25328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75984 ÷ 4 = 18996) | 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 (75984 ÷ 6 = 12664) | 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 (75984 ÷ 8 = 9498) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (75984 ÷ 12 = 6332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75984 a prime number?
No. 75984 = × 3 × 1583, so it is divisible by 2.
What are the factors of 75984?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1583, 3166, 4749, 6332, 9498, 12664, 18996, 25328, 37992, 75984.
What is 75984 in binary?
10010100011010000 (hexadecimal 128D0, octal 224320).
What is the square root of 75984?
About 275.6520, exactly 4√4749.
Is 75984 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 75984?
It is a composite number with 20 divisors.