The number 55872
55872 is a composite number with 42 divisors. Its prime factorisation is × × 97. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 55872.
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How to work it out
- 1
What is special about 55872: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
55872 is composite. Its prime factorisation is
- 3
The divisors add up to 161798; without 55872 itself that is 105926, so 55872 is abundant (105926 is more than 55872). Euler's totient φ(55872) = 18432 numbers up to 55872 share no factor with it.
- 4
The digits of 55872 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 153 steps to reach 1.
LaTeX source of the formulas on this page
\[ 55872 = 2^{6} \times 3^{2} \times 97 \]55872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 161798 |
| Euler totient φ(n) | 18432 |
| Square | 3121680384 |
| Cube | 174414526414848 |
| Square root | 236.372587 (= 24√97) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 153 |
| Scientific notation | 5.5872 × |
55872 in other forms
| Form | Value |
|---|---|
| In words | fifty-five thousand eight hundred and seventy-two |
| Binary (base 2) | 1101101001000000 |
| Octal (base 8) | 155100 |
| Hexadecimal (base 16) | DA40 |
| Base 3 | 2211122100 |
| As time | 55872 seconds = 15 h 31 min 12 s |
Is 55872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (55872 ÷ 2 = 27936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (55872 ÷ 3 = 18624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (55872 ÷ 4 = 13968) | 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 (55872 ÷ 6 = 9312) | 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 | Yes (55872 ÷ 8 = 6984) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (55872 ÷ 9 = 6208) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (55872 ÷ 12 = 4656) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 55872 a prime number?
No. 55872 = × × 97, so it is divisible by 2.
What are the factors of 55872?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 97, 144, 192, 194, 288, 291, 388, 576, 582, 776, 873, 1164, 1552, 1746, 2328, 3104, 3492, 4656, 6208, 6984, 9312, 13968, 18624, 27936, 55872.
What is 55872 in binary?
1101101001000000 (hexadecimal DA40, octal 155100).
What is the square root of 55872?
About 236.3726, exactly 24√97.
Is 55872 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 55872?
55872 is a happy number: repeatedly adding the squares of its digits reaches 1.