The number 23968
23968 is a composite number with 24 divisors. Its prime factorisation is × 7 × 107. Divisors (24): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 107, 112, 214, 224, 428, 749 … 23968.
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How to work it out
- 1
What is special about 23968: a Harshad number: divisible by its digit sum 28.
- 2
23968 is composite. Its prime factorisation is
- 3
The divisors add up to 54432; without 23968 itself that is 30464, so 23968 is abundant (30464 is more than 23968). Euler's totient φ(23968) = 10176 numbers up to 23968 share no factor with it.
- 4
The digits of 23968 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23968 = 2^{5} \times 7 \times 107 \]23968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 54432 |
| Euler totient φ(n) | 10176 |
| Square | 574465024 |
| Cube | 13768777695232 |
| Square root | 154.816020 (= 4√1498) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3968 × |
23968 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand nine hundred and sixty-eight |
| Binary (base 2) | 101110110100000 |
| Octal (base 8) | 56640 |
| Hexadecimal (base 16) | 5DA0 |
| Base 3 | 1012212201 |
| As time | 23968 seconds = 6 h 39 min 28 s |
Is 23968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23968 ÷ 2 = 11984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23968 ÷ 4 = 5992) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (23968 ÷ 7 = 3424) | 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 (23968 ÷ 8 = 2996) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23968 a prime number?
No. 23968 = × 7 × 107, so it is divisible by 2.
What are the factors of 23968?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 107, 112, 214, 224, 428, 749, 856, 1498, 1712, 2996, 3424, 5992, 11984, 23968.
What is 23968 in binary?
101110110100000 (hexadecimal 5DA0, octal 56640).
What is the square root of 23968?
About 154.8160, exactly 4√1498.
Is 23968 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 23968?
23968 is a Harshad number: divisible by its digit sum 28.