The number 32772
32772 is a composite number with 12 divisors. Its prime factorisation is × 3 × 2731. Divisors (12): 1, 2, 3, 4, 6, 12, 2731, 5462, 8193, 10924, 16386, 32772.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
32772 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32772 is composite. Its prime factorisation is
- 3
The divisors add up to 76496; without 32772 itself that is 43724, so 32772 is abundant (43724 is more than 32772). Euler's totient φ(32772) = 10920 numbers up to 32772 share no factor with it.
- 4
The digits of 32772 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32772 = 2^{2} \times 3 \times 2731 \]32772 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 76496 |
| Euler totient φ(n) | 10920 |
| Square | 1074003984 |
| Cube | 35197258563648 |
| Square root | 181.030384 (= 2√8193) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.2772 × |
32772 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and seventy-two |
| Binary (base 2) | 1000000000000100 |
| Octal (base 8) | 100004 |
| Hexadecimal (base 16) | 8004 |
| Base 3 | 1122221210 |
| As time | 32772 seconds = 9 h 6 min 12 s |
Is 32772 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32772 ÷ 2 = 16386) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32772 ÷ 3 = 10924) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32772 ÷ 4 = 8193) | 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 | Yes (32772 ÷ 6 = 5462) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32772 ÷ 12 = 2731) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32772 a prime number?
No. 32772 = × 3 × 2731, so it is divisible by 2.
What are the factors of 32772?
1, 2, 3, 4, 6, 12, 2731, 5462, 8193, 10924, 16386, 32772.
What is 32772 in binary?
1000000000000100 (hexadecimal 8004, octal 100004).
What is the square root of 32772?
About 181.0304, exactly 2√8193.
Is 32772 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 32772?
It is a composite number with 12 divisors.