The number 72432
72432 is a composite number with 30 divisors. Its prime factorisation is × × 503. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 503 … 72432.
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How to work it out
- 1
What is special about 72432: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72432 is composite. Its prime factorisation is
- 3
The divisors add up to 203112; without 72432 itself that is 130680, so 72432 is abundant (130680 is more than 72432). Euler's totient φ(72432) = 24096 numbers up to 72432 share no factor with it.
- 4
The digits of 72432 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72432 = 2^{4} \times 3^{2} \times 503 \]72432 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 203112 |
| Euler totient φ(n) | 24096 |
| Square | 5246394624 |
| Cube | 380006855405568 |
| Square root | 269.131938 (= 12√503) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.2432 × |
72432 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred and thirty-two |
| Binary (base 2) | 10001101011110000 |
| Octal (base 8) | 215360 |
| Hexadecimal (base 16) | 11AF0 |
| Base 3 | 10200100200 |
| As time | 72432 seconds = 20 h 7 min 12 s |
Is 72432 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72432 ÷ 2 = 36216) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72432 ÷ 3 = 24144) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72432 ÷ 4 = 18108) | 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 (72432 ÷ 6 = 12072) | 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 (72432 ÷ 8 = 9054) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72432 ÷ 9 = 8048) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72432 ÷ 12 = 6036) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72432 a prime number?
No. 72432 = × × 503, so it is divisible by 2.
What are the factors of 72432?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 503, 1006, 1509, 2012, 3018, 4024, 4527, 6036, 8048, 9054, 12072, 18108, 24144, 36216, 72432.
What is 72432 in binary?
10001101011110000 (hexadecimal 11AF0, octal 215360).
What is the square root of 72432?
About 269.1319, exactly 12√503.
Is 72432 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72432?
72432 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.