The number 15984
15984 is a composite number with 40 divisors. Its prime factorisation is × × 37. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 37, 48, 54 … 15984.
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How to work it out
- 1
What is special about 15984: a Harshad number: divisible by its digit sum 27.
- 2
15984 is composite. Its prime factorisation is
- 3
The divisors add up to 47120; without 15984 itself that is 31136, so 15984 is abundant (31136 is more than 15984). Euler's totient φ(15984) = 5184 numbers up to 15984 share no factor with it.
- 4
The digits of 15984 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15984 = 2^{4} \times 3^{3} \times 37 \]15984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 47120 |
| Euler totient φ(n) | 5184 |
| Square | 255488256 |
| Cube | 4083724283904 |
| Square root | 126.427845 (= 12√111) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 53 |
| Scientific notation | 1.5984 × |
15984 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand nine hundred and eighty-four |
| Binary (base 2) | 11111001110000 |
| Octal (base 8) | 37160 |
| Hexadecimal (base 16) | 3E70 |
| Base 3 | 210221000 |
| As time | 15984 seconds = 4 h 26 min 24 s |
Is 15984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15984 ÷ 2 = 7992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15984 ÷ 3 = 5328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15984 ÷ 4 = 3996) | 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 (15984 ÷ 6 = 2664) | 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 (15984 ÷ 8 = 1998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (15984 ÷ 9 = 1776) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15984 ÷ 12 = 1332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15984 a prime number?
No. 15984 = × × 37, so it is divisible by 2.
What are the factors of 15984?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 37, 48, 54, 72, 74, 108, 111, 144, 148, 216, 222, 296, 333, 432, 444, 592, 666, 888, 999, 1332, 1776, 1998, 2664, 3996, 5328, 7992, 15984.
What is 15984 in binary?
11111001110000 (hexadecimal 3E70, octal 37160).
What is the square root of 15984?
About 126.4278, exactly 12√111.
Is 15984 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 15984?
15984 is a Harshad number: divisible by its digit sum 27.