The number 17424
17424 is a perfect square (132²). Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44 … 17424.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17424: a perfect square (132²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
17424 is composite. Its prime factorisation is
- 3
The divisors add up to 53599; without 17424 itself that is 36175, so 17424 is abundant (36175 is more than 17424). Euler's totient φ(17424) = 5280 numbers up to 17424 share no factor with it.
- 4
The digits of 17424 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 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17424 = 2^{4} \times 3^{2} \times 11^{2} \]17424 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 53599 |
| Euler totient φ(n) | 5280 |
| Square | 303595776 |
| Cube | 5289852801024 |
| Square root | 132 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.7424 × |
| Perfect power |
17424 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand four hundred and twenty-four |
| Binary (base 2) | 100010000010000 |
| Octal (base 8) | 42020 |
| Hexadecimal (base 16) | 4410 |
| Base 3 | 212220100 |
| As time | 17424 seconds = 4 h 50 min 24 s |
Is 17424 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17424 ÷ 2 = 8712) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17424 ÷ 3 = 5808) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17424 ÷ 4 = 4356) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17424 ÷ 6 = 2904) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (17424 ÷ 8 = 2178) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (17424 ÷ 9 = 1936) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (17424 ÷ 11 = 1584) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (17424 ÷ 12 = 1452) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17424 a prime number?
No. 17424 = × × , so it is divisible by 2.
What are the factors of 17424?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 121, 132, 144, 176, 198, 242, 264, 363, 396, 484, 528, 726, 792, 968, 1089, 1452, 1584, 1936, 2178, 2904, 4356, 5808, 8712, 17424.
What is 17424 in binary?
100010000010000 (hexadecimal 4410, octal 42020).
What is the square root of 17424?
132, because 132 × 132 = 17424.
Is 17424 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 17424?
17424 is a perfect square (132²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.