The number 32984
32984 is a composite number with 32 divisors. Its prime factorisation is × 7 × 19 × 31. Divisors (32): 1, 2, 4, 7, 8, 14, 19, 28, 31, 38, 56, 62, 76, 124, 133, 152 … 32984.
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How to work it out
- 1
32984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32984 is composite. Its prime factorisation is
- 3
The divisors add up to 76800; without 32984 itself that is 43816, so 32984 is abundant (43816 is more than 32984). Euler's totient φ(32984) = 12960 numbers up to 32984 share no factor with it.
- 4
The digits of 32984 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32984 = 2^{3} \times 7 \times 19 \times 31 \]32984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 76800 |
| Euler totient φ(n) | 12960 |
| Square | 1087944256 |
| Cube | 35884753339904 |
| Square root | 181.614977 (= 2√8246) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.2984 × |
32984 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand nine hundred and eighty-four |
| Binary (base 2) | 1000000011011000 |
| Octal (base 8) | 100330 |
| Hexadecimal (base 16) | 80D8 |
| Base 3 | 1200020122 |
| As time | 32984 seconds = 9 h 9 min 44 s |
Is 32984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32984 ÷ 2 = 16492) | 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 (32984 ÷ 4 = 8246) | 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 | Yes (32984 ÷ 7 = 4712) | 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 (32984 ÷ 8 = 4123) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 6) | 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 32984 a prime number?
No. 32984 = × 7 × 19 × 31, so it is divisible by 2.
What are the factors of 32984?
1, 2, 4, 7, 8, 14, 19, 28, 31, 38, 56, 62, 76, 124, 133, 152, 217, 248, 266, 434, 532, 589, 868, 1064, 1178, 1736, 2356, 4123, 4712, 8246, 16492, 32984.
What is 32984 in binary?
1000000011011000 (hexadecimal 80D8, octal 100330).
What is the square root of 32984?
About 181.6150, exactly 2√8246.
Is 32984 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 32984?
It is a composite number with 32 divisors.