The number 32788
32788 is a composite number with 12 divisors. Its prime factorisation is × 7 × 1171. Divisors (12): 1, 2, 4, 7, 14, 28, 1171, 2342, 4684, 8197, 16394, 32788.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32788: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 28.
- 2
32788 is composite. Its prime factorisation is
- 3
The divisors add up to 65632; without 32788 itself that is 32844, so 32788 is abundant (32844 is more than 32788). Euler's totient φ(32788) = 14040 numbers up to 32788 share no factor with it.
- 4
The digits of 32788 add up to 28, 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
\[ 32788 = 2^{2} \times 7 \times 1171 \]32788 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 65632 |
| Euler totient φ(n) | 14040 |
| Square | 1075052944 |
| Cube | 35248835927872 |
| Square root | 181.074570 (= 2√8197) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.2788 × |
32788 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and eighty-eight |
| Binary (base 2) | 1000000000010100 |
| Octal (base 8) | 100024 |
| Hexadecimal (base 16) | 8014 |
| Base 3 | 1122222101 |
| As time | 32788 seconds = 9 h 6 min 28 s |
Is 32788 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32788 ÷ 2 = 16394) | 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 (32788 ÷ 4 = 8197) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | Yes (32788 ÷ 7 = 4684) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | 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 32788 a prime number?
No. 32788 = × 7 × 1171, so it is divisible by 2.
What are the factors of 32788?
1, 2, 4, 7, 14, 28, 1171, 2342, 4684, 8197, 16394, 32788.
What is 32788 in binary?
1000000000010100 (hexadecimal 8014, octal 100024).
What is the square root of 32788?
About 181.0746, exactly 2√8197.
Is 32788 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 32788?
32788 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 28.