The number 23364
23364 is a composite number with 36 divisors. Its prime factorisation is × × 11 × 59. Divisors (36): 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 59, 66, 99 … 23364.
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How to work it out
- 1
What is special about 23364: a Harshad number: divisible by its digit sum 18.
- 2
23364 is composite. Its prime factorisation is
- 3
The divisors add up to 65520; without 23364 itself that is 42156, so 23364 is abundant (42156 is more than 23364). Euler's totient φ(23364) = 6960 numbers up to 23364 share no factor with it.
- 4
The digits of 23364 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 82 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23364 = 2^{2} \times 3^{2} \times 11 \times 59 \]23364 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 65520 |
| Euler totient φ(n) | 6960 |
| Square | 545876496 |
| Cube | 12753858452544 |
| Square root | 152.852870 (= 6√649) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 82 |
| Scientific notation | 2.3364 × |
23364 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand three hundred and sixty-four |
| Binary (base 2) | 101101101000100 |
| Octal (base 8) | 55504 |
| Hexadecimal (base 16) | 5B44 |
| Base 3 | 1012001100 |
| As time | 23364 seconds = 6 h 29 min 24 s |
Is 23364 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23364 ÷ 2 = 11682) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23364 ÷ 3 = 7788) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23364 ÷ 4 = 5841) | 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 (23364 ÷ 6 = 3894) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (23364 ÷ 9 = 2596) | 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 (23364 ÷ 11 = 2124) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23364 ÷ 12 = 1947) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23364 a prime number?
No. 23364 = × × 11 × 59, so it is divisible by 2.
What are the factors of 23364?
1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 59, 66, 99, 118, 132, 177, 198, 236, 354, 396, 531, 649, 708, 1062, 1298, 1947, 2124, 2596, 3894, 5841, 7788, 11682, 23364.
What is 23364 in binary?
101101101000100 (hexadecimal 5B44, octal 55504).
What is the square root of 23364?
About 152.8529, exactly 6√649.
Is 23364 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 23364?
23364 is a Harshad number: divisible by its digit sum 18.