The number 31988
31988 is a composite number with 12 divisors. Its prime factorisation is × 11 × 727. Divisors (12): 1, 2, 4, 11, 22, 44, 727, 1454, 2908, 7997, 15994, 31988.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31988: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
31988 is composite. Its prime factorisation is
- 3
The divisors add up to 61152; without 31988 itself that is 29164, so 31988 is deficient (29164 is less than 31988). Euler's totient φ(31988) = 14520 numbers up to 31988 share no factor with it.
- 4
The digits of 31988 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31988 = 2^{2} \times 11 \times 727 \]31988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 61152 |
| Euler totient φ(n) | 14520 |
| Square | 1023232144 |
| Cube | 32731149822272 |
| Square root | 178.851894 (= 2√7997) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1988 × |
31988 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and eighty-eight |
| Binary (base 2) | 111110011110100 |
| Octal (base 8) | 76364 |
| Hexadecimal (base 16) | 7CF4 |
| Base 3 | 1121212202 |
| As time | 31988 seconds = 8 h 53 min 8 s |
Is 31988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31988 ÷ 2 = 15994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31988 ÷ 4 = 7997) | 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 2) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 (31988 ÷ 11 = 2908) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31988 a prime number?
No. 31988 = × 11 × 727, so it is divisible by 2.
What are the factors of 31988?
1, 2, 4, 11, 22, 44, 727, 1454, 2908, 7997, 15994, 31988.
What is 31988 in binary?
111110011110100 (hexadecimal 7CF4, octal 76364).
What is the square root of 31988?
About 178.8519, exactly 2√7997.
Is 31988 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 31988?
31988 is a happy number: repeatedly adding the squares of its digits reaches 1.