The number 1888
1888 is a composite number with 12 divisors. Its prime factorisation is × 59. Divisors (12): 1, 2, 4, 8, 16, 32, 59, 118, 236, 472, 944, 1888.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1888: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1888 is composite. Its prime factorisation is
- 3
The divisors add up to 3780; without 1888 itself that is 1892, so 1888 is abundant (1892 is more than 1888). Euler's totient φ(1888) = 928 numbers up to 1888 share no factor with it.
- 4
The digits of 1888 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1888 = 2^{5} \times 59 \]1888 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3780 |
| Euler totient φ(n) | 928 |
| Square | 3564544 |
| Cube | 6729859072 |
| Square root | 43.451122 (= 4√118) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.888 × |
1888 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and eighty-eight |
| Roman numerals | MDCCCLXXXVIII |
| Binary (base 2) | 11101100000 |
| Octal (base 8) | 3540 |
| Hexadecimal (base 16) | 760 |
| Base 3 | 2120221 |
| As time | 1888 seconds = 31 min 28 s |
Is 1888 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1888 ÷ 2 = 944) | 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 (1888 ÷ 4 = 472) | 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 | 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 (1888 ÷ 8 = 236) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 7) | 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 1888 a prime number?
No. 1888 = × 59, so it is divisible by 2.
What are the factors of 1888?
1, 2, 4, 8, 16, 32, 59, 118, 236, 472, 944, 1888.
What is 1888 in binary?
11101100000 (hexadecimal 760, octal 3540).
What is the square root of 1888?
About 43.4511, exactly 4√118.
What is 1888 in Roman numerals?
MDCCCLXXXVIII.
Is 1888 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 1888?
1888 is a happy number: repeatedly adding the squares of its digits reaches 1.