The number 31824
31824 is a composite number with 60 divisors. Its prime factorisation is × × 13 × 17. Divisors (60): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 17, 18, 24, 26, 34, 36 … 31824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31824: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
31824 is composite. Its prime factorisation is
- 3
The divisors add up to 101556; without 31824 itself that is 69732, so 31824 is abundant (69732 is more than 31824). Euler's totient φ(31824) = 9216 numbers up to 31824 share no factor with it.
- 4
The digits of 31824 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31824 = 2^{4} \times 3^{2} \times 13 \times 17 \]31824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 101556 |
| Euler totient φ(n) | 9216 |
| Square | 1012766976 |
| Cube | 32230296244224 |
| Square root | 178.392825 (= 12√221) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 28 |
| Scientific notation | 3.1824 × |
31824 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand eight hundred and twenty-four |
| Binary (base 2) | 111110001010000 |
| Octal (base 8) | 76120 |
| Hexadecimal (base 16) | 7C50 |
| Base 3 | 1121122200 |
| As time | 31824 seconds = 8 h 50 min 24 s |
Is 31824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31824 ÷ 2 = 15912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31824 ÷ 3 = 10608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31824 ÷ 4 = 7956) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31824 ÷ 6 = 5304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (31824 ÷ 8 = 3978) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31824 ÷ 9 = 3536) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31824 ÷ 12 = 2652) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31824 a prime number?
No. 31824 = × × 13 × 17, so it is divisible by 2.
What are the factors of 31824?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 17, 18, 24, 26, 34, 36, 39, 48, 51, 52, 68, 72, 78, 102, 104, 117, 136, 144, 153, 156, 204, 208, 221, 234, 272, 306, 312, 408, 442, 468, 612, 624, 663, 816, 884, 936, 1224, 1326, 1768, 1872, 1989, 2448, 2652, 3536, 3978, 5304, 7956, 10608, 15912, 31824.
What is 31824 in binary?
111110001010000 (hexadecimal 7C50, octal 76120).
What is the square root of 31824?
About 178.3928, exactly 12√221.
Is 31824 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 31824?
31824 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.