The number 31968
31968 is a composite number with 48 divisors. Its prime factorisation is × × 37. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 37, 48 … 31968.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31968: a Harshad number: divisible by its digit sum 27.
- 2
31968 is composite. Its prime factorisation is
- 3
The divisors add up to 95760; without 31968 itself that is 63792, so 31968 is abundant (63792 is more than 31968). Euler's totient φ(31968) = 10368 numbers up to 31968 share no factor with it.
- 4
The digits of 31968 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31968 = 2^{5} \times 3^{3} \times 37 \]31968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 95760 |
| Euler totient φ(n) | 10368 |
| Square | 1021953024 |
| Cube | 32669794271232 |
| Square root | 178.795973 (= 12√222) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1968 × |
31968 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and sixty-eight |
| Binary (base 2) | 111110011100000 |
| Octal (base 8) | 76340 |
| Hexadecimal (base 16) | 7CE0 |
| Base 3 | 1121212000 |
| As time | 31968 seconds = 8 h 52 min 48 s |
Is 31968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31968 ÷ 2 = 15984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31968 ÷ 3 = 10656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31968 ÷ 4 = 7992) | 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 | Yes (31968 ÷ 6 = 5328) | 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 | Yes (31968 ÷ 8 = 3996) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31968 ÷ 9 = 3552) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31968 ÷ 12 = 2664) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31968 a prime number?
No. 31968 = × × 37, so it is divisible by 2.
What are the factors of 31968?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 37, 48, 54, 72, 74, 96, 108, 111, 144, 148, 216, 222, 288, 296, 333, 432, 444, 592, 666, 864, 888, 999, 1184, 1332, 1776, 1998, 2664, 3552, 3996, 5328, 7992, 10656, 15984, 31968.
What is 31968 in binary?
111110011100000 (hexadecimal 7CE0, octal 76340).
What is the square root of 31968?
About 178.7960, exactly 12√222.
Is 31968 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 31968?
31968 is a Harshad number: divisible by its digit sum 27.