The number 32967
32967 is a composite number with 20 divisors. Its prime factorisation is × 11 × 37. Divisors (20): 1, 3, 9, 11, 27, 33, 37, 81, 99, 111, 297, 333, 407, 891, 999, 1221 … 32967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32967: a Harshad number: divisible by its digit sum 27.
- 2
32967 is composite. Its prime factorisation is
- 3
The divisors add up to 55176; without 32967 itself that is 22209, so 32967 is deficient (22209 is less than 32967). Euler's totient φ(32967) = 19440 numbers up to 32967 share no factor with it.
- 4
The digits of 32967 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 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32967 = 3^{4} \times 11 \times 37 \]32967 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 55176 |
| Euler totient φ(n) | 19440 |
| Square | 1086823089 |
| Cube | 35829296775063 |
| Square root | 181.568169 (= 9√407) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.2967 × |
32967 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand nine hundred and sixty-seven |
| Binary (base 2) | 1000000011000111 |
| Octal (base 8) | 100307 |
| Hexadecimal (base 16) | 80C7 |
| Base 3 | 1200020000 |
| As time | 32967 seconds = 9 h 9 min 27 s |
Is 32967 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32967 ÷ 3 = 10989) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32967 ÷ 9 = 3663) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (32967 ÷ 11 = 2997) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32967 a prime number?
No. 32967 = × 11 × 37, so it is divisible by 3.
What are the factors of 32967?
1, 3, 9, 11, 27, 33, 37, 81, 99, 111, 297, 333, 407, 891, 999, 1221, 2997, 3663, 10989, 32967.
What is 32967 in binary?
1000000011000111 (hexadecimal 80C7, octal 100307).
What is the square root of 32967?
About 181.5682, exactly 9√407.
Is 32967 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 32967?
32967 is a Harshad number: divisible by its digit sum 27.