The number 432
432 is a composite number with 20 divisors. Its prime factorisation is × . Divisors (20): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 432.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 432: a Harshad number: divisible by its digit sum 9.
- 2
432 is composite. Its prime factorisation is
- 3
The divisors add up to 1240; without 432 itself that is 808, so 432 is abundant (808 is more than 432). Euler's totient φ(432) = 144 numbers up to 432 share no factor with it.
- 4
The digits of 432 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 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 432 = 2^{4} \times 3^{3} \]432 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 1240 |
| Euler totient φ(n) | 144 |
| Square | 186624 |
| Cube | 80621568 |
| Square root | 20.784610 (= 12√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 115 |
| Scientific notation | 4.32 × |
432 in other forms
| Form | Value |
|---|---|
| In words | four hundred and thirty-two |
| Roman numerals | CDXXXII |
| Binary (base 2) | 110110000 |
| Octal (base 8) | 660 |
| Hexadecimal (base 16) | 1B0 |
| Base 3 | 121000 |
| As time | 432 seconds = 7 min 12 s |
Is 432 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (432 ÷ 2 = 216) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (432 ÷ 3 = 144) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (432 ÷ 4 = 108) | 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 (432 ÷ 6 = 72) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (432 ÷ 8 = 54) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (432 ÷ 9 = 48) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (432 ÷ 12 = 36) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 432 a prime number?
No. 432 = × , so it is divisible by 2.
What are the factors of 432?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432.
What is 432 in binary?
110110000 (hexadecimal 1B0, octal 660).
What is the square root of 432?
About 20.7846, exactly 12√3.
What is 432 in Roman numerals?
CDXXXII.
Is 432 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 432?
432 is a Harshad number: divisible by its digit sum 9.