The number 32724
32724 is a composite number with 30 divisors. Its prime factorisation is × × 101. Divisors (30): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 101, 108, 162, 202 … 32724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32724: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
32724 is composite. Its prime factorisation is
- 3
The divisors add up to 86394; without 32724 itself that is 53670, so 32724 is abundant (53670 is more than 32724). Euler's totient φ(32724) = 10800 numbers up to 32724 share no factor with it.
- 4
The digits of 32724 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 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32724 = 2^{2} \times 3^{4} \times 101 \]32724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 86394 |
| Euler totient φ(n) | 10800 |
| Square | 1070860176 |
| Cube | 35042828399424 |
| Square root | 180.897761 (= 18√101) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.2724 × |
32724 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and twenty-four |
| Binary (base 2) | 111111111010100 |
| Octal (base 8) | 77724 |
| Hexadecimal (base 16) | 7FD4 |
| Base 3 | 1122220000 |
| As time | 32724 seconds = 9 h 5 min 24 s |
Is 32724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32724 ÷ 2 = 16362) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32724 ÷ 3 = 10908) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32724 ÷ 4 = 8181) | 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 (32724 ÷ 6 = 5454) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32724 ÷ 9 = 3636) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32724 ÷ 12 = 2727) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32724 a prime number?
No. 32724 = × × 101, so it is divisible by 2.
What are the factors of 32724?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 101, 108, 162, 202, 303, 324, 404, 606, 909, 1212, 1818, 2727, 3636, 5454, 8181, 10908, 16362, 32724.
What is 32724 in binary?
111111111010100 (hexadecimal 7FD4, octal 77724).
What is the square root of 32724?
About 180.8978, exactly 18√101.
Is 32724 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32724?
32724 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.