The number 19488
19488 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 29. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42 … 19488.
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How to work it out
- 1
What is special about 19488: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
19488 is composite. Its prime factorisation is
- 3
The divisors add up to 60480; without 19488 itself that is 40992, so 19488 is abundant (40992 is more than 19488). Euler's totient φ(19488) = 5376 numbers up to 19488 share no factor with it.
- 4
The digits of 19488 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 136 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19488 = 2^{5} \times 3 \times 7 \times 29 \]19488 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 60480 |
| Euler totient φ(n) | 5376 |
| Square | 379782144 |
| Cube | 7401194422272 |
| Square root | 139.599427 (= 4√1218) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 136 |
| Scientific notation | 1.9488 × |
19488 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand four hundred and eighty-eight |
| Binary (base 2) | 100110000100000 |
| Octal (base 8) | 46040 |
| Hexadecimal (base 16) | 4C20 |
| Base 3 | 222201210 |
| As time | 19488 seconds = 5 h 24 min 48 s |
Is 19488 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19488 ÷ 2 = 9744) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19488 ÷ 3 = 6496) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19488 ÷ 4 = 4872) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (19488 ÷ 6 = 3248) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (19488 ÷ 7 = 2784) | 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 (19488 ÷ 8 = 2436) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (19488 ÷ 12 = 1624) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19488 a prime number?
No. 19488 = × 3 × 7 × 29, so it is divisible by 2.
What are the factors of 19488?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 84, 87, 96, 112, 116, 168, 174, 203, 224, 232, 336, 348, 406, 464, 609, 672, 696, 812, 928, 1218, 1392, 1624, 2436, 2784, 3248, 4872, 6496, 9744, 19488.
What is 19488 in binary?
100110000100000 (hexadecimal 4C20, octal 46040).
What is the square root of 19488?
About 139.5994, exactly 4√1218.
Is 19488 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 19488?
19488 is a happy number: repeatedly adding the squares of its digits reaches 1.