The number 32752
32752 is a composite number with 20 divisors. Its prime factorisation is × 23 × 89. Divisors (20): 1, 2, 4, 8, 16, 23, 46, 89, 92, 178, 184, 356, 368, 712, 1424, 2047 … 32752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32752: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
32752 is composite. Its prime factorisation is
- 3
The divisors add up to 66960; without 32752 itself that is 34208, so 32752 is abundant (34208 is more than 32752). Euler's totient φ(32752) = 15488 numbers up to 32752 share no factor with it.
- 4
The digits of 32752 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32752 = 2^{4} \times 23 \times 89 \]32752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 66960 |
| Euler totient φ(n) | 15488 |
| Square | 1072693504 |
| Cube | 35132857643008 |
| Square root | 180.975136 (= 4√2047) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.2752 × |
32752 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and fifty-two |
| Binary (base 2) | 111111111110000 |
| Octal (base 8) | 77760 |
| Hexadecimal (base 16) | 7FF0 |
| Base 3 | 1122221001 |
| As time | 32752 seconds = 9 h 5 min 52 s |
Is 32752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32752 ÷ 2 = 16376) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32752 ÷ 4 = 8188) | 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 4) | 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 (32752 ÷ 8 = 4094) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32752 a prime number?
No. 32752 = × 23 × 89, so it is divisible by 2.
What are the factors of 32752?
1, 2, 4, 8, 16, 23, 46, 89, 92, 178, 184, 356, 368, 712, 1424, 2047, 4094, 8188, 16376, 32752.
What is 32752 in binary?
111111111110000 (hexadecimal 7FF0, octal 77760).
What is the square root of 32752?
About 180.9751, exactly 4√2047.
Is 32752 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 32752?
32752 is a happy number: repeatedly adding the squares of its digits reaches 1.