The number 32864
32864 is a composite number with 24 divisors. Its prime factorisation is × 13 × 79. Divisors (24): 1, 2, 4, 8, 13, 16, 26, 32, 52, 79, 104, 158, 208, 316, 416, 632 … 32864.
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How to work it out
- 1
What is special about 32864: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
32864 is composite. Its prime factorisation is
- 3
The divisors add up to 70560; without 32864 itself that is 37696, so 32864 is abundant (37696 is more than 32864). Euler's totient φ(32864) = 14976 numbers up to 32864 share no factor with it.
- 4
The digits of 32864 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32864 = 2^{5} \times 13 \times 79 \]32864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 70560 |
| Euler totient φ(n) | 14976 |
| Square | 1080042496 |
| Cube | 35494516588544 |
| Square root | 181.284307 (= 4√2054) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.2864 × |
32864 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand eight hundred and sixty-four |
| Binary (base 2) | 1000000001100000 |
| Octal (base 8) | 100140 |
| Hexadecimal (base 16) | 8060 |
| Base 3 | 1200002012 |
| As time | 32864 seconds = 9 h 7 min 44 s |
Is 32864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32864 ÷ 2 = 16432) | 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 (32864 ÷ 4 = 8216) | 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 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 (32864 ÷ 8 = 4108) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32864 a prime number?
No. 32864 = × 13 × 79, so it is divisible by 2.
What are the factors of 32864?
1, 2, 4, 8, 13, 16, 26, 32, 52, 79, 104, 158, 208, 316, 416, 632, 1027, 1264, 2054, 2528, 4108, 8216, 16432, 32864.
What is 32864 in binary?
1000000001100000 (hexadecimal 8060, octal 100140).
What is the square root of 32864?
About 181.2843, exactly 4√2054.
Is 32864 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 32864?
32864 is a happy number: repeatedly adding the squares of its digits reaches 1.