The number 31185
31185 is a composite number with 40 divisors. Its prime factorisation is × 5 × 7 × 11. Divisors (40): 1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 35, 45, 55, 63, 77, 81 … 31185.
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How to work it out
- 1
What is special about 31185: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
31185 is composite. Its prime factorisation is
- 3
The divisors add up to 69696; without 31185 itself that is 38511, so 31185 is abundant (38511 is more than 31185). Euler's totient φ(31185) = 12960 numbers up to 31185 share no factor with it.
- 4
The digits of 31185 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 147 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31185 = 3^{4} \times 5 \times 7 \times 11 \]31185 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 69696 |
| Euler totient φ(n) | 12960 |
| Square | 972504225 |
| Cube | 30327544256625 |
| Square root | 176.592752 (= 9√385) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 147 |
| Scientific notation | 3.1185 × |
31185 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand one hundred and eighty-five |
| Binary (base 2) | 111100111010001 |
| Octal (base 8) | 74721 |
| Hexadecimal (base 16) | 79D1 |
| Base 3 | 1120210000 |
| As time | 31185 seconds = 8 h 39 min 45 s |
Is 31185 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31185 ÷ 3 = 10395) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31185 ÷ 5 = 6237) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (31185 ÷ 7 = 4455) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31185 ÷ 9 = 3465) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (31185 ÷ 11 = 2835) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31185 a prime number?
No. 31185 = × 5 × 7 × 11, so it is divisible by 3.
What are the factors of 31185?
1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 35, 45, 55, 63, 77, 81, 99, 105, 135, 165, 189, 231, 297, 315, 385, 405, 495, 567, 693, 891, 945, 1155, 1485, 2079, 2835, 3465, 4455, 6237, 10395, 31185.
What is 31185 in binary?
111100111010001 (hexadecimal 79D1, octal 74721).
What is the square root of 31185?
About 176.5928, exactly 9√385.
Is 31185 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 31185?
31185 is a happy number: repeatedly adding the squares of its digits reaches 1.