The number 19764
19764 is a composite number with 30 divisors. Its prime factorisation is × × 61. Divisors (30): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 61, 81, 108, 122, 162 … 19764.
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How to work it out
- 1
What is special about 19764: a Harshad number: divisible by its digit sum 27.
- 2
19764 is composite. Its prime factorisation is
- 3
The divisors add up to 52514; without 19764 itself that is 32750, so 19764 is abundant (32750 is more than 19764). Euler's totient φ(19764) = 6480 numbers up to 19764 share no factor with it.
- 4
The digits of 19764 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 136 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19764 = 2^{2} \times 3^{4} \times 61 \]19764 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 52514 |
| Euler totient φ(n) | 6480 |
| Square | 390615696 |
| Cube | 7720128615744 |
| Square root | 140.584494 (= 18√61) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 136 |
| Scientific notation | 1.9764 × |
19764 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand seven hundred and sixty-four |
| Binary (base 2) | 100110100110100 |
| Octal (base 8) | 46464 |
| Hexadecimal (base 16) | 4D34 |
| Base 3 | 1000010000 |
| As time | 19764 seconds = 5 h 29 min 24 s |
Is 19764 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19764 ÷ 2 = 9882) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19764 ÷ 3 = 6588) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19764 ÷ 4 = 4941) | 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 (19764 ÷ 6 = 3294) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (19764 ÷ 9 = 2196) | 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 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (19764 ÷ 12 = 1647) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19764 a prime number?
No. 19764 = × × 61, so it is divisible by 2.
What are the factors of 19764?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 61, 81, 108, 122, 162, 183, 244, 324, 366, 549, 732, 1098, 1647, 2196, 3294, 4941, 6588, 9882, 19764.
What is 19764 in binary?
100110100110100 (hexadecimal 4D34, octal 46464).
What is the square root of 19764?
About 140.5845, exactly 18√61.
Is 19764 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 19764?
19764 is a Harshad number: divisible by its digit sum 27.