The number 23820
23820 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 397. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 397, 794, 1191, 1588 … 23820.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23820: a Harshad number: divisible by its digit sum 15.
- 2
23820 is composite. Its prime factorisation is
- 3
The divisors add up to 66864; without 23820 itself that is 43044, so 23820 is abundant (43044 is more than 23820). Euler's totient φ(23820) = 6336 numbers up to 23820 share no factor with it.
- 4
The digits of 23820 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23820 = 2^{2} \times 3 \times 5 \times 397 \]23820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 66864 |
| Euler totient φ(n) | 6336 |
| Square | 567392400 |
| Cube | 13515286968000 |
| Square root | 154.337293 (= 2√5955) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 144 |
| Scientific notation | 2.382 × |
23820 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand eight hundred and twenty |
| Binary (base 2) | 101110100001100 |
| Octal (base 8) | 56414 |
| Hexadecimal (base 16) | 5D0C |
| Base 3 | 1012200020 |
| As time | 23820 seconds = 6 h 37 min 0 s |
Is 23820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23820 ÷ 2 = 11910) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23820 ÷ 3 = 7940) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23820 ÷ 4 = 5955) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (23820 ÷ 5 = 4764) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (23820 ÷ 6 = 3970) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (23820 ÷ 10 = 2382) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23820 ÷ 12 = 1985) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23820 a prime number?
No. 23820 = × 3 × 5 × 397, so it is divisible by 2.
What are the factors of 23820?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 397, 794, 1191, 1588, 1985, 2382, 3970, 4764, 5955, 7940, 11910, 23820.
What is 23820 in binary?
101110100001100 (hexadecimal 5D0C, octal 56414).
What is the square root of 23820?
About 154.3373, exactly 2√5955.
Is 23820 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 23820?
23820 is a Harshad number: divisible by its digit sum 15.