The number 55968
55968 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 53. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 53 … 55968.
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How to work it out
- 1
What is special about 55968: a Harshad number: divisible by its digit sum 33.
- 2
55968 is composite. Its prime factorisation is
- 3
The divisors add up to 163296; without 55968 itself that is 107328, so 55968 is abundant (107328 is more than 55968). Euler's totient φ(55968) = 16640 numbers up to 55968 share no factor with it.
- 4
The digits of 55968 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 55968 = 2^{5} \times 3 \times 11 \times 53 \]55968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 163296 |
| Euler totient φ(n) | 16640 |
| Square | 3132417024 |
| Cube | 175315115999232 |
| Square root | 236.575569 (= 4√3498) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 122 |
| Scientific notation | 5.5968 × |
55968 in other forms
| Form | Value |
|---|---|
| In words | fifty-five thousand nine hundred and sixty-eight |
| Binary (base 2) | 1101101010100000 |
| Octal (base 8) | 155240 |
| Hexadecimal (base 16) | DAA0 |
| Base 3 | 2211202220 |
| As time | 55968 seconds = 15 h 32 min 48 s |
Is 55968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (55968 ÷ 2 = 27984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (55968 ÷ 3 = 18656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (55968 ÷ 4 = 13992) | 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 (55968 ÷ 6 = 9328) | 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 | Yes (55968 ÷ 8 = 6996) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (55968 ÷ 11 = 5088) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (55968 ÷ 12 = 4664) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 55968 a prime number?
No. 55968 = × 3 × 11 × 53, so it is divisible by 2.
What are the factors of 55968?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 53, 66, 88, 96, 106, 132, 159, 176, 212, 264, 318, 352, 424, 528, 583, 636, 848, 1056, 1166, 1272, 1696, 1749, 2332, 2544, 3498, 4664, 5088, 6996, 9328, 13992, 18656, 27984, 55968.
What is 55968 in binary?
1101101010100000 (hexadecimal DAA0, octal 155240).
What is the square root of 55968?
About 236.5756, exactly 4√3498.
Is 55968 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 55968?
55968 is a Harshad number: divisible by its digit sum 33.