The number 55752
55752 is a composite number with 32 divisors. Its prime factorisation is × 3 × 23 × 101. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 101, 138, 184, 202 … 55752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 55752: a Harshad number: divisible by its digit sum 24.
- 2
55752 is composite. Its prime factorisation is
- 3
The divisors add up to 146880; without 55752 itself that is 91128, so 55752 is abundant (91128 is more than 55752). Euler's totient φ(55752) = 17600 numbers up to 55752 share no factor with it.
- 4
The digits of 55752 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 55752 = 2^{3} \times 3 \times 23 \times 101 \]55752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 146880 |
| Euler totient φ(n) | 17600 |
| Square | 3108285504 |
| Cube | 173293133419008 |
| Square root | 236.118614 (= 2√13938) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 60 |
| Scientific notation | 5.5752 × |
55752 in other forms
| Form | Value |
|---|---|
| In words | fifty-five thousand seven hundred and fifty-two |
| Binary (base 2) | 1101100111001000 |
| Octal (base 8) | 154710 |
| Hexadecimal (base 16) | D9C8 |
| Base 3 | 2211110220 |
| As time | 55752 seconds = 15 h 29 min 12 s |
Is 55752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (55752 ÷ 2 = 27876) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (55752 ÷ 3 = 18584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (55752 ÷ 4 = 13938) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (55752 ÷ 6 = 9292) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (55752 ÷ 8 = 6969) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (55752 ÷ 12 = 4646) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 55752 a prime number?
No. 55752 = × 3 × 23 × 101, so it is divisible by 2.
What are the factors of 55752?
1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 101, 138, 184, 202, 276, 303, 404, 552, 606, 808, 1212, 2323, 2424, 4646, 6969, 9292, 13938, 18584, 27876, 55752.
What is 55752 in binary?
1101100111001000 (hexadecimal D9C8, octal 154710).
What is the square root of 55752?
About 236.1186, exactly 2√13938.
Is 55752 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 55752?
55752 is a Harshad number: divisible by its digit sum 24.