The number 32000
32000 is a composite number with 36 divisors. Its prime factorisation is × . Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125 … 32000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32000: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.
- 2
32000 is composite. Its prime factorisation is
- 3
The divisors add up to 79716; without 32000 itself that is 47716, so 32000 is abundant (47716 is more than 32000). Euler's totient φ(32000) = 12800 numbers up to 32000 share no factor with it.
- 4
The digits of 32000 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32000 = 2^{8} \times 5^{3} \]32000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 79716 |
| Euler totient φ(n) | 12800 |
| Square | 1024000000 |
| Cube | 32768000000000 |
| Square root | 178.885438 (= 80√5) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 116 |
| Scientific notation | 3.2 × |
32000 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand |
| Binary (base 2) | 111110100000000 |
| Octal (base 8) | 76400 |
| Hexadecimal (base 16) | 7D00 |
| Base 3 | 1121220012 |
| As time | 32000 seconds = 8 h 53 min 20 s |
Is 32000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32000 ÷ 2 = 16000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32000 ÷ 4 = 8000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32000 ÷ 5 = 6400) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (32000 ÷ 8 = 4000) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32000 ÷ 10 = 3200) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32000 a prime number?
No. 32000 = × , so it is divisible by 2.
What are the factors of 32000?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 640, 800, 1000, 1280, 1600, 2000, 3200, 4000, 6400, 8000, 16000, 32000.
What is 32000 in binary?
111110100000000 (hexadecimal 7D00, octal 76400).
What is the square root of 32000?
About 178.8854, exactly 80√5.
Is 32000 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 32000?
32000 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.