The number 1588
1588 is a composite number with 6 divisors. Its prime factorisation is × 397. Divisors (6): 1, 2, 4, 397, 794, 1588.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1588 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1588 is composite. Its prime factorisation is
- 3
The divisors add up to 2786; without 1588 itself that is 1198, so 1588 is deficient (1198 is less than 1588). Euler's totient φ(1588) = 792 numbers up to 1588 share no factor with it.
- 4
The digits of 1588 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1588 = 2^{2} \times 397 \]1588 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 2786 |
| Euler totient φ(n) | 792 |
| Square | 2521744 |
| Cube | 4004529472 |
| Square root | 39.849718 (= 2√397) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.588 × |
1588 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and eighty-eight |
| Roman numerals | MDLXXXVIII |
| Binary (base 2) | 11000110100 |
| Octal (base 8) | 3064 |
| Hexadecimal (base 16) | 634 |
| Base 3 | 2011211 |
| As time | 1588 seconds = 26 min 28 s |
Is 1588 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1588 ÷ 2 = 794) | 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 (1588 ÷ 4 = 397) | 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 6) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 4) | 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 1588 a prime number?
No. 1588 = × 397, so it is divisible by 2.
What are the factors of 1588?
1, 2, 4, 397, 794, 1588.
What is 1588 in binary?
11000110100 (hexadecimal 634, octal 3064).
What is the square root of 1588?
About 39.8497, exactly 2√397.
What is 1588 in Roman numerals?
MDLXXXVIII.
Is 1588 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 1588?
It is a composite number with 6 divisors.