The number 32364
32364 is a composite number with 36 divisors. Its prime factorisation is × × 29 × 31. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 29, 31, 36, 58, 62, 87, 93, 116 … 32364.
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How to work it out
- 1
What is special about 32364: a Harshad number: divisible by its digit sum 18.
- 2
32364 is composite. Its prime factorisation is
- 3
The divisors add up to 87360; without 32364 itself that is 54996, so 32364 is abundant (54996 is more than 32364). Euler's totient φ(32364) = 10080 numbers up to 32364 share no factor with it.
- 4
The digits of 32364 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 191 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32364 = 2^{2} \times 3^{2} \times 29 \times 31 \]32364 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 87360 |
| Euler totient φ(n) | 10080 |
| Square | 1047428496 |
| Cube | 33898975844544 |
| Square root | 179.899972 (= 6√899) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 191 |
| Scientific notation | 3.2364 × |
32364 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand three hundred and sixty-four |
| Binary (base 2) | 111111001101100 |
| Octal (base 8) | 77154 |
| Hexadecimal (base 16) | 7E6C |
| Base 3 | 1122101200 |
| As time | 32364 seconds = 8 h 59 min 24 s |
Is 32364 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32364 ÷ 2 = 16182) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32364 ÷ 3 = 10788) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32364 ÷ 4 = 8091) | 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 (32364 ÷ 6 = 5394) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32364 ÷ 9 = 3596) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32364 ÷ 12 = 2697) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32364 a prime number?
No. 32364 = × × 29 × 31, so it is divisible by 2.
What are the factors of 32364?
1, 2, 3, 4, 6, 9, 12, 18, 29, 31, 36, 58, 62, 87, 93, 116, 124, 174, 186, 261, 279, 348, 372, 522, 558, 899, 1044, 1116, 1798, 2697, 3596, 5394, 8091, 10788, 16182, 32364.
What is 32364 in binary?
111111001101100 (hexadecimal 7E6C, octal 77154).
What is the square root of 32364?
About 179.9000, exactly 6√899.
Is 32364 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32364?
32364 is a Harshad number: divisible by its digit sum 18.