The number 4032
4032 is a composite number with 42 divisors. Its prime factorisation is × × 7. Divisors (42): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32 … 4032.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4032: a Harshad number: divisible by its digit sum 9.
- 2
4032 is composite. Its prime factorisation is
- 3
The divisors add up to 13208; without 4032 itself that is 9176, so 4032 is abundant (9176 is more than 4032). Euler's totient φ(4032) = 1152 numbers up to 4032 share no factor with it.
- 4
The digits of 4032 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4032 = 2^{6} \times 3^{2} \times 7 \]4032 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 13208 |
| Euler totient φ(n) | 1152 |
| Square | 16257024 |
| Cube | 65548320768 |
| Square root | 63.498031 (= 24√7) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 113 |
| Scientific notation | 4.032 × |
4032 in other forms
| Form | Value |
|---|---|
| In words | four thousand and thirty-two |
| Binary (base 2) | 111111000000 |
| Octal (base 8) | 7700 |
| Hexadecimal (base 16) | FC0 |
| Base 3 | 12112100 |
| As time | 4032 seconds = 1 h 7 min 12 s |
Is 4032 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4032 ÷ 2 = 2016) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4032 ÷ 3 = 1344) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4032 ÷ 4 = 1008) | 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 (4032 ÷ 6 = 672) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (4032 ÷ 7 = 576) | 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 (4032 ÷ 8 = 504) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (4032 ÷ 9 = 448) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4032 ÷ 12 = 336) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4032 a prime number?
No. 4032 = × × 7, so it is divisible by 2.
What are the factors of 4032?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 144, 168, 192, 224, 252, 288, 336, 448, 504, 576, 672, 1008, 1344, 2016, 4032.
What is 4032 in binary?
111111000000 (hexadecimal FC0, octal 7700).
What is the square root of 4032?
About 63.4980, exactly 24√7.
Is 4032 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 4032?
4032 is a Harshad number: divisible by its digit sum 9.